NASA 1E 1- 70 6d
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X-661-74-71 NASA 1E 1- 70 6d CHARGE COMPOSITION OF HIGH ENERGY HEAVY PRIMARY COSMIC RAY NUCLEI ROBERT D. PRICE A--X-70622) CHAE COPOSITION OF 74-21412 HIGH ENERGY HEAVY PRIMARy COSMIC BAY OUCLEI Ph.D. Thesis - Catholic Univ. of Am. (NASA) -- ~ p HC $11.75 CSCL 03B / ?. lUnclas G3/29 36515 MARCH 1974 - GODDARD SPACE FLIGHT CENTER GREENBELT, MARYLAND
Transcript of NASA 1E 1- 70 6d
X-661-74-71
NASA 1E 1- 70 6d
CHARGE COMPOSITION OF HIGH
ENERGY HEAVY PRIMARYCOSMIC RAY NUCLEI
ROBERT D. PRICE
A--X-70622) CHAE COPOSITION OF 74-21412HIGH ENERGY HEAVY PRIMARy COSMIC BAYOUCLEI Ph.D. Thesis - Catholic Univ. ofAm. (NASA) -- ~ p HC $11.75 CSCL 03B
/ ?. lUnclasG3/29 36515
MARCH 1974
- GODDARD SPACE FLIGHT CENTERGREENBELT, MARYLAND
For information concerning availabilityof this document contact:
Technical Information Division, Code 250Goddard Space Flight CenterGreenbelt, Maryland 20771
(Telephone 301-982-4488)
THE CATHOLIC UNIVERSITY OF AMERICA
CHARGE COMPOSITION OF HIGH ENERGY HEAVY PRIMARY COSMIC RAY NUCLEI
A DISSERTATION
Submitted to the Faculty of The
Engineering and Architecture School
Of The Catholic University of AmericaIn Partial Fulfillment of the Requirements
For the DegreeDoctor of Philosophy
byRobert D. Price
Washington, D.C.1974
/
ACKNOWLEDGEMENTS
I wish to express my sincere thanks to the many people who contributed
to the success of this research, which was conducted in its entirety with
the High Energy Cosmic Ray Experiment Grou- of tLe Laboratory for High
Energy Astrophysics at NASA/Goddard Space Flight Center. In particular,
I wish to thank Dr. F. B. McDonald, Chief, LHEA, for giving me the oppor-
tunity to conduct this research while an employee of his laboratory, for
encouraging me to obtain the Ph.D. degree, for allowing me the time
necessary to complete the degree, for continued patience with me throughout
the duration of the research, and for providing all the facilities necessary
for the conduct and completion of this work. Indeed, I am indebted to him
for the privilege of working in the LHEA.
It is with deepest gratitude that I acknowledge my advisor, Dr. J. F.
Ormes, for suggesting the topic of investigation, directing the research,
and providing continuous guidance and valuable advice throughout. Without
his assistance, this dissertation would not have been possible. It is a
pleasure to thank Dr. V. K. Balasubrahmanyan, who acted as a second advisor
to me, for his suggestions and constructive criticisms.
One of the advantages gained from working in the LHEA was to be able
to draw information and advice directly from many experts in the field of
cosmic ray physics via "private communication". I have benefited greatly
from numerous invaluable and helpful discussions with the following people
regarding many phases of this work: Dr. L. A. Fisk on solar modulation,
Dr. R. Ramaty on interstellar propagation, Dr. D. Reames on nuclear inter-
actions, and Dr. T. T. von Rosenvinge on high energy charge composition
of cosmic rays.PRECEDING PAGE BLANK NOT FILMED
iii
From the start this has been a group project. Therefore the entire
staff of the HECRE Group is to be thanked for their close support and
skillful assistance: Mr. J. Laws, electronics engineer, who was respon-
sible for the electronics design and provided leadership and support for,
all electronics development and testing; and the technicians, Messrs.
G. Cooper, R. Greer, M. Powers, T. Puig, J. Purvis, and L. Stonebraker
who provided invaluable technical support in the form of experience,
initiative, responsibility for fabrication and assembly of the experiment
components, and long hours which contributed directly to the success of
the experiment.
Messrs. A. Thompson, H. Trexel, and F. Shaffer were responsible for
the initial mechanical design of the experiment. They are to be thanked
for their continued swift and excellent quality drafting support, both
for the mechanical design and layout of the experiment and for the draw-
ings used in this dissertation. Appreciation is also expressed to Ms.
B. Dallas 'for the patient, diligent, and careful preparation of this
manuscript. Additional secretarial support was provided by Ms. B. Shavatt,
Ms. M. A. Spruill, and Ms. G. Evans.
Lastly, but certainly most important to me, I wish to recognize the
contributions of my parents, Mr. and Mrs. W. H. Price, that have helped
to make this goal possible. They have always stressed to me the value of
obtaining as full and complete an education as possible. They gave me the
opportunity to pursue a higher education by providing me with financial
assistance at great sacrifice to themselves during my undergraduate educa-
tion. They have been a constant source of encouragement and moral support
throughout the trying years of my graduate education. I am deeply
iv
indebted to them and wish to express my sincerest gratitude for their aid.
To them I dedicate this dissertation.
v
ABSTRACT
A detailed study of the charge composition of primary cosmic radia-
tion for about 5000 charged nuclei from neon to iron with energies
greater than 1.16 GeV/nucleon is presented. Integral flux values of
10:Zs14 = 9.58 x 10 -1, 15Z~19 = 1.80 x 10 -', 20!Z523 - 1.15 x 10-1, and
24-Z928 = 2.37 x 10 - particles/m-sec-ster for rigidity greater than
4.9 GV and 10:Zsl4 = 1.54 x 100, 15-Z;19 - 2.90 x 10 - 1, 20!Z923 = 2.10
x 10-1 and 24!Z28 = 3.60 x 10-1 particles/ma-sec-ster for rigidity
greater than 3.25 GV are reported and compared to other recent measure-
ments at similar geomagnetic latitude. These values are obtained after
corrections have been made for detector dependences, atmospheric attenuation
and solar modulation. New values of 38.5, 32.4, 23.7, and 16.8 g/cm2 for
the attenuation mean free paths in air for these same charge groups are
presented.
An ionization spectrometer was used to measure the charge spectrum.
This detector system consisted of 3 parts: (1) a charge identification
module with 2784 cm -ster geometry factor, consisting of two plastic scin-
tillators, one inorganic scintillator (CsI), and one Lucite plastic
Cerenkov radiator, (2) a four-grid (2 X-Y pairs) spark chamber to determine
each particle's trajectory through the spectrometer, and (3) an energy
deposition module consisting of layers of tungsten, and iron interspersed
with scintillator for measuring ionization energy loss. This detector
measured the charge of a nucleus to an accuracy estimated to be . +0.7 of
a unit charge. The spectrometer was flown from Holloman Air Force Base,
New Mexico (5.0 GV rigidity cutoff) and floated at an altitude of 7.4 g/cm2
for 16 hours.
vi
The observed charge composition has.been corrected for detector
dependences and atmospheric attenuation. This charge distribution,
extrapolated back to the source using an exponential path length distri-
bution of pure hydrogen, is consistent with a mean amount of matter of
5 g/cm. The results of this propagation back to the source imply the
source is predominantly iron, neon (Ne/Fe = 1.44), magnesium (Mg/Fe =
1.68), silicon (Si/Fe = 1.38), with admixtures of sulfur (S/Fe = 0.29),
and calcium (Ca/Fe = 0.18), all other elements of charge between 10 Z.26
being absent at the source and being produced by cosmic ray fragmentation
in interstellar hydrogen. This source charge composition is quite similar
to the solar system abundances with the exception of neon, sulfur, and
argon. It is consistent with the predictions of explosive nucleosynthesis
in highly evolved massive stars, i.e. a supernova origin for energetic heavy
cosmic rays.
vii
TABLE OF CONTENTS
Page
ABSTRACT ....... . . . .. . . . . . . . . . . . . vi
LIST OF TABLES . . . . ...... . . . . . . . . . . . . ....... x
LIST OF FIGURES . . . . . . . . . . . . . . . . . xi
Chapter
I, Introduction . . ................. . . . . 1
II. Description of Experiment . . . . . . . . . . . . . . ... . 13
A. Charge Identification Module .. .......... . . .13
1. Discussion . . . . . . . . . . . . . . . . . . . . 132. Coincidence scintillators . . . . . . . . . . . . . . 163. Cerenkov radiator . . . . . . . . . . . . . . . . 194. Cesium iodide scintillator . . . . . . . . . . . . . 22
B. Spark Chamber Module .. . . . . . . . . . . . . . . 23
C. Ionization Spectrometer ............. . . . . . 27
III. Data Analysis .......... .. ........ . . . .. 31
A. Discussion . . . . . . . j. ... .. .. . . . . . . . . .31
B. Angle Corrections . ..... ........... . . .. 33
1. Zenith angle compensation . . . . . . . . . . . . . . 332. Azimuthal angle compensation . . . . . . . . . . . . 36
C. Area Correction . . ..... . . . . . . . . . . . . . 37
D. Nonlinearities of Plastics and PHA's . . . . . . . . . 39
1. Plastics . . . ........... ........ .. . 392. PHA's . ....... .......... . . . .. ..... . 41
E. Landau Fluctuations . . . . . . ................... 42
F. Four Dimensional Hyper-ellipsoidal Charge Determination . 50
G. Background Correction ............. . . . . . 57
H. Correction for Overlying Atmosphere .......... . 63
I. Correction for Solar Modulation ... .... ....... 74
viii
Page
IV. Results ..... ......... . . . . . . . . . . . 76
A. Fluxes at Top of Atmosphere ........ ...... . 76
B. Charge Composition, 10 < Z : 28 . ........... . 85
1. Present experiment ... . .......... . .... 85
2. Comparison with other measurements ... . . . . . . 88
V. Interpretation of Experimental Results . ........ . . 96
A. Extrapolation Back to Source . ... . . . ......... . 96
B. Cosmic Ray Age - Amount of Matter in Interstellar
Space ............ ... . . . . . . . . . .111
C. Comparison to Solar System Abundances .. ........ .113
D. Possible Source of Primary Cosmic Radiation . .. ... . .122
VI. Summary/Conclusions . . . . ... . . . . . . . . . . . . .129
Appendix A. Electronics and Threshold Settings . ....... . .135
Appendix B. Definition of "Good Event" in Spark Chamber . . .143
Appendix C. Solar Modulation . ... ......... . . . .150
Bibliography .. .... . . . . . . . ... . . . . . . . . .. 156
ix
LIST OF TABLES
Table Page
1. Statistics on Landau Distribution for RelativisticZ - 25 Nuclei ............ .... . .... . 48
2. Interaction Mean Free Paths in Plastic, Cesium Iodide,and Aluminum ...... ........... ....... 62
3a. Atmospheric Attenuation Mean Free Paths . . . . . . . . . . . 67b. Absorption Mean Free Paths in Air . . . . . . . . . . . . .. 68
4. Fluxes of Cosmic Ray Nuclei from This Experiment . . . ... 79
5. Fluxes of Cosmic Ray Nuclei from This ExperimentCompared to Other Measurements ..... ... ..... . . 81
6. Charge Composition, 10 < Z < 28, from This Experiment . . . . 86
7. Charge Composition Measured in This Experiment Comparedto Other Results . . . . ......... * *......... .. 90
8. Fragmentation Probabilities for Collisions with Hydrogen . . .101
9. Absorption Mean Free Paths in Hydrogen . . ....... . . . .... 103
10. Comparison of Deduced Source Composition of Several Authors ..114
11. Comparison of Solar System Abundances to Cosmic Ray SourceAbundances . . . . . .. . . ......................... . 118
12. Comparison of Deduced Cosmic Ray Source Composition toExplosive Nucleosynthesis Predictions . . ......... . . . . .125
X
LIST OF FIGURES
Figure Page
1. Schematic Diagram of the High Energy Cosmic RayExperiment, an Ionization Spectrometer . .... . . . . ...11
2. Schematic Diagram of Charge Identification Module
(CIM), the Top Module of the High Energy CosmicRay Ionization Spectrometer Experiment .... . . . . . . 14
3. Zenith Angle Distribution of Detected Carbon Nuclei(Histogram Points) Compared to the Differential
Geometry of the Charge Identification Module (Solid
Line) as a Function of Zenith Angle . . .. .......... . 25
4. Schematic Diagram of a Cascade Shower of an Iron NucleusThrough the Ionization Spectrometer . . . . . . . . . . . 29
5. Relative Response of the 4 Charge Detectors Plotted asa Function of Zenith Angle. Solid Line RepresentsTheoretical Correction (sec 0), Crosses Represent Experi-mental Data (Carbon Nuclei). Note That the Scale for theCerenkov Response Curve on the Right Hand Side isDifferent from the Other 3 Detectors. . ... . . . . . . 34
6. Variations in Pulse Height as Percentage Deviations fromthe Mean Response as a Function of Position and LinearDimension Across the Area of the Scintillator, S1 . . . . 38
7. Comparison of Nonlinear Output (Points) of the 4 ChargeDetector Elements to Theoretical Linear Response (SolidLine) Expected for Charges 4-9 . ........... . 40
8. Example of a Landau Distribution for the Most ProbableEnergy Loss in a Thin Scintillator . .......... 44
9. The Intrinsic Resolution Due to Landau StatisticalFluctuations in Energy Loss as a Function of Charge,Z, for Various Energies (Solid Curves), Compared to theResolution Required to Separate Adjacent Charges (DashedCurve). The Curve Labelled 0 = 0.95 is Applicable tothe Data in This Paper . ................ 46
10. Two Dimensional Pulse Height Matrix, Scintillators Sland S2. Pulse Heights have been Corrected for DetectorDependences but Background Events have not been Removed.. 51
11. Charge Histogram, Z - 10-26, Taken from Two DimensionalMatrix, SI-82, of Corrected Pulse Heights with BackgroundRemoved . . . . . . . . . . . . . . . . . . . . . . . . . 56
xi
Figure Page
12. Two Dimensional Pulse Height Matrix, ScintillatorsS1 and S2,with Background Events Removed . ........ 59
13. Relative Flux of Charge Groups as a Function of Depthin the Atmosphere. The Slope of the Least Squares Fitto the Data (Solid Line) Yields the Atmospheric Atten-uation Mean Free Path . . . . . . . . . . . . . . .. 65
14. Charge Composition, Z = 10-28, at the Top of theAtmosphere, Normalized to the Iron Abundance . ...... 87
15. Charge Composition, Z = 10-28, at the Top of theAtmosphere Compared to the Review Article Summariesof Webber (1972) and Tsao et al. (1973), Normalizedto the Iron Abundance . .......... . . . . . . . 89
16. Charge Composition, Z = 10-28, at the Top of theAtmosphere Compared to the Low Energy Results ofCartwright et al. (1973) and Lezniak et al. (1970),Normalized to Iron. ... ...... . . . . ..... . .. 94
17. Exponential Distribution of Cosmic Ray Path Lengths,dN/dx - e-o .aox. . . . . . . . . . . . . . . . . . . 106
18. Comparison of Cosmic Ray Source Composition to theCosmic Ray Charge Composition at the Top of theAtmosphere ................... .... . 108
19. Comparison of Cosmic Ray Source Composition to SolarSystem Abundances, Normalized to Iron . ......... 119
20. Comparison of Deduced Cosmic Ray Source Composition tothe Predictions of Explosive Nucleosynthesis, Normalizedto Irqn ................... .. ..... 127
Al. Electronics Block Diagram . ...... . ..... . . . 136
A2. Data Handling and Telemetry Block Diagram . ...... . 137
A3. Logic Diagram Showing Event Acceptance Criteria andTriggering Requirements . .. . . .. . . . ....... . 142
BI. Example of a Well Defined Trajectory Through the SparkChamber for a Carbon Nucleus Event. Note the SatelliteSparks Near the Trajectory Which are Presumably Due toKnock On Electrons. This Figure has been Created from aSlide Taken of a Graphic Display Unit Which Can be Usedto Look at Individual Events . ............. 148
xii
I. INTRODUCTION
Primary galactic cosmic radiation consists largely of ionized nuclei
of the elements hydrogen through iron (Z = 1 to 26) with non-zero fluxes
of elements throughout the periodic table rt to ucanium (Z = 92) and
beyond, possibly as high as Z - 114 (Fowler et al., 1967, 1970; Fleischer
et al., 1967 a, b) with energies ranging from 108 to 1020 eV/nucleon. The
chemical composition and energy spectra of these multiply charged nuclei
have been the subject of intensive study since their discovery in 1947
(Freier et al., 1948a, b; Bradt and Peters, 1948). But the problems of
the origin of these particles and their propagation through the inter-
stellar medium, although the topic of much theoretical discussion since
their.discovery, remain essentially unsolved.
The study of primary cosmic radiation, i.e. particle astronomy, is
an important source of astrophysical information regarding the physical
characteristics of our space-time environment and complements the knowl-
edge obtained by radio, optical, x-ray, and y-ray astronomy techniques.
These energetic nuclei represent a sample of matter that has survived a
complex series of physical processes which are comparatively common in the
universe but that are not very well understood nor well defined at
present. A general picture of the history of a cosmic ray particle which
has struck the Earth begins with its production in some unknown way..
There are reasons for believing that cosmic rays are produced and acceler-
ated in the expanding envelopes of exploding supernovae, or in the fields
of pulsars. Considerable changes of the production composition may occur
during acceleration in the source. For example, injection energies may
depend on the relative ionization potential of the various nuclides;
1
2
nucleon reactions may occur during acceleration; escape of particles from
an acceleration region, if that region is bounded, may depend on the mass
and charge of the individual nucleus. It is thus possible that the compo-
sition of the accelerated sample is differcnt from that present in the
source region. These esoteric possibilities will be neglected in this
thesis since there is no real understanding of them and they are specu-
lation at beet. It will be assumed then that the abundances of the.
various types of particles reveal something of the nature of processes
and the characteristics of the region where they are occurring.
The next phase experienced by the nuclei is a combination of physical
processes which can be included under.the heading of propagation through
the interstellar medium. The propagation of a cosmic ray nucleus through
the Galaxy subjects the charged particle to the effects of the magnetic
fields traversed. The magnetic fields randomize the arrival direction of
cosmic rays, which explains why cosmic rays are observed to arrive at the
Earth isotropically. The particles also suffer chance encounters with
matter in space (mostly hydrogen atoms) which produce the effects of energy
loss due to ionization and collision. Some of the heavy nuclei will under-
go catastrophic collisions or nuclear interactions with interstellar matter
causing them to break up into nuclei of smaller charge, thus changing their
identity, and hence altering the source composition. The magnitude of all
these effects depends on the nature and amount of matter traversed, which
in turn depends on the configuration and strength of the magnetic fields
experienced by the nuclei during their traversal of the medium.
Finally, as the cosmic ray particle comes within some 10 to 100 A.U.
of the sun it encounters the solar wind, a plasma streaming out of the sun
with its frozen-in magnetic field which tends to sweep out lower energy
3
particles. The interaction of the nuclei with the solar environment
leads to a solar modulation of the intensity of the nuclei, decreasing
the intensity detected near Earth compared to that outside the solar
system and possibly reducing their energy. The magnitude of solar modu-
lation is dependent on the charge-to-mass ratio, the energy of the
nuclei, and the level of solar activity. Even at times of low solar
activity, there is considerable uncertainty regarding the amount and form
of the residual modulation. After running upstream against this solar
wind, the particle enters the nearly dipole magnetic field of the earth
which acts to deflect the charged particle. If it has enough energy to
penetrate the magnetic field, it enters the earth's atmosphere and even-
tually interacts with one or several air molecules, ending its journey.
But if the primary cosmic ray nucleus should survive this rigorous
journey and be detected, since it is the only direct sample of matter orig-
inating outside the solar system that can be observed, it will bring with
it many "clues" about the galaxy which, when combined with a knowledge of
the galaxy's physical structure, such as the spiral arms and halo, and
physical processes, such as pulsars and supernovae, and then properly
interpreted, will reveal its own history as well as increase knowledge of
the galaxy itself.
The experimental observables, i.e. the "clues" available for measure-
ment, in cosmic radiation are the charge composition, the energy spectra
of the nuclear components, anisotropy in arrival direction, and temporal
variations. Because of the complexity of the processes undergone by
cosmic rays between their origin and their observation, it is attractive
and probably essential to observe all of these interrelated quantities
under comparable conditions at one time. At present all experimental
observables have not been measured in one experiment, hence data collec-
ted thus far has just established its own consistency.
The balloon-borne experiment to be described in this paper has been
designed to observe the energy spectra and charge composition of elements
of approximately the lower one quarter of the periodic table. (The event
collection time needed to delineate the features of anisotropy and temp-
poral variations await the application of similar experiments to long
duration satellite flights). The piecemeal studies of primary cosmic
radiation that have been conducted to date have advanced knowledge of the
galaxy, and its radiation, however, by increasing knowledge of the origin
and propagation of cosmic rays. The predictions of any theory of primary
cosmic radiation must match the "corrected" values of the experimental
observables, i.e. the values obtained after the observed values have been
adjusted for detector dependences, solar modulation, and propagational
effects. Since the predictions are based on a model of the galaxy, match-
ing the predictions pins down the model applicable to the Galaxy. Fea-
tures of low energy spectral and charge composition studies have been
determined by various experiments mentioned in the next paragraph. How-
ever, as indicated in later paragraphs, features determined from high
energy spectral and charge composition studies have given more fruitful
results when applied to galactic models.
Knowledge of the low and medium energy range (--10 to 109 eV/nucleon)
is quite extensive, and detailed observations and theoretical studies of
the charge composition and the energy spectra have been made in this
energy interval. (Fan et al., 1968; Price et al., 1967, 1968, 1970). It
has been considered that these cosmic ray nuclei of the lowest observable
energies provide the best clues concerning their sources and their propa-
5
gation to Earth. But the experimental results of studies of low energy
particles has demonstrated that theoretical conclusions about their rela-
tive energy spectra are not borne out. (Comstock et al., 1966, 1969;
Freier and Waddington, 1968a, 1968b; Fichtel and Reames, 1968). There
are a number of reasons for this failure of agreement, but only two of
the more important ones will be briefly presented here. Firstly, a solar
demodulation correction, based on the solar activity at the time of meas-
urement, must be applied to the data to obtain fluxes outside the solar
system. This correction is large in the low energy region. Secondly,
present models of particle propagation through the galaxy may break down
at low energies if the diffusion coefficients are n-dependent, which would
result in a-dependent path lengths. The best worked out theories about the
relative charge abundances apply to the energy range 109 to 1012 eV/nuc.
This is so for three reasons: (1) solar modulation is small and can be
reasonably well accounted for, (Webber, 1967a) (2) fragmentation para-
meters are.generally constant in this range and thus more likely to be
known, (Cleghorn, 1967), (3) at these energies fragmentation and ioniza-
tion loss have small effect on the shape of the energy spectrum, (Beck and
Yiou, 1968).
The high energy regions, i.e. 109 eV/nuc., should offer more promise
for the solution of the major problems confronting cosmic ray physicists.
Above 1.0 GeV/nuc., however, data on chemical composition and energy spec-
tra are very sparse. Known features of the primary cosmic radiation in
this energy range include the following: (1) the spectrum of each cosmic
ray element is described by a power law in total energy/nucleon, the
index of the integral spectrum varying from -1.1 to -2.0, depending on
the element. (2) the presence of lithium-beryllium-boron in large rela-
6
tive abundances, (3) the high abundance of heavy nuclei (Z z 10) relative
to hydrogen and helium, and (4) the intensity variation between even- and
odd- numbered nuclei.
The two most abundant components of the cosmic radiation, proton and
helium nuclei, have been studied extensively, and their energy spectra are
well known over a wide range of energies. (See Anand et al., 1968; Fan
et al., 1968; and Ormes, 1967). The most reliable and statistically sig-
nificant measurements in the charge range 2ZEl0 have been made by
von Rosenvinge et al. (1969 a, b), Freier and Waddington (1968a), Webber
and Ormes (1967), Ormes et al. (1970), and Ryan et al. (1972)
The observed numbers of cosmic ray nuclei in the light heavy (10 Zi14),
medium heavy (15Z 19),land very heavy (Zt20).region have been insufficient
to permit an element-by-element study of their energy spectra. This situ-
ation was partly remedied by studies of the VH spectrum (see Webber and
Ormes, 1967; von Rosenvinge, 1969; Freier and Waddington, 1968a; Mewaldt
et al., 1971), where considerable attention was directed toward determin-
ing the detailed energy spectra of heavy nuclei in primary cosmic radia-
tion. But there is still a paucity of measurements of the intensity of
individual heavy nuclei above 1,0 GeV/nuc.
Recent measurements (Juliusson et al., 1972; Ormes and Balasubrahmanyan
1973; Smith et al., 1973; and Webber et al., 1973) of cosmic ray energy
spectra of small groups of elements Z;6 with energies up to 100 GeV/nuc.
have revealed startling new features which have not been included in prior
theories of the origin of cosmic rays and their propagation in interstellar
space. These results have indicated that: (1) the relative nuclear compo-
sition of cosmic rays changes with energy in such a manner that the ratio
of galactic secondary nuclei to galactic primary nuclei decreases as
7
energy increases. (Juliusson et al., 1972; Ormes and Balasubrahmanyan,
1973; Smith et al., 1973; and Webber et al., 1973a, and (2) the differen-
tial energy spectra of individual nuclei are well represented by smooth
power laws in total energy/nuc.with spectral indices ranging from -2.5 to
-3.0, i.e. no significant structure, breaks, or steepening of the spectra
have been observed at energies beyond the region of influence of solar
modulation (Ryan et al., 1972 and Juliusson, 1973).
Several recent charge composition studies, which in general are
integral energy measurements of individual heavy elements (Z _ 10), have
succeeded in achieving nearly unique charge resolution out to iron.
(Mewaldt et al., 1971; Juliusson et'al., 1972; Smith et al., 1973; and
Webber et al., 1973a). The results of these experiments indicate a charge
composition for primary cosmic radiation that is different from that
observed in the solar system.
Considerable interest is.attached to the energy spectra and charge
composition of nuclei (Z 6) because these studies of energetic heavy
galactic cosmic radiation provide unique information on the source regions
of cosmic radiation, on propagation and possibly acceleration of cosmic
radiation, on interactions of cosmic ray particles in the tenuous inter-
stellar gas, on the amount of material traversed before escaping the
Galaxy, and on the age of cosmic rays. The interpretations of the experi-
mental results of these studies are illustrated in the next few sentences.
The results cited previously of energy spectra studies are interrelated,
and are relevant to the origin and propagation of cosmic rays in that they
can be utilized to decide whether cosmic radiation has a local origin or,
to go to the other extreme, is extragalactic in origin, and whether con-
finement in the galaxy is energy dependent. For example, attempts to
8
explain the decreasing ratio with energy of secondary nuclei to primary
nuclei lead to the conclusion that high energy cosmic rays must have
traversed less matter than low energy cosmic rays. Since theoretical as
well as experimental results indicate that spallation cross sections for
daughter nuclei do not depend strongly on energy above 1 GeV/nuc., the
observed decrease in the ratio must mean less matter is traversed at high
energy as opposed to low energy rather than being due to the propaga-
tional effects of collision. Further implications could be (1) very enLr-
getic nuclei are produced predominantly by sources which are close to the
solar system; or (2) primary cosmic ray nuclei are extragalactic in origin
but secondaries are produced in the, galaxy and have energy dependent con-
finement; or (3) cosmic radiation is of galactic origin and confinement
in the galaxy is energy dependent. The results of charge composition
studies have provided more constraints on the origin and propagation of
cosmic radiation in that they can be utilized to decide amongst various
possible sources of cosmic rays as well as place restrictions on cosmic
ray propagation models. For example, the nuclei in the charge range
10Z 30, which includes the very significant iron region, are those in
the primary cosmic radiation, with the exception of the very rare Z-30,
that have the shortest interaction mean free paths and greatest rates of
energy loss through ionization in traversing matter. As a consequence
of the large interaction cross sections, i.e. short interaction mean free
paths, the relative abundances of these heavy cosmic ray nuclei are very
sensitive to the amount of interstellar matter that they have traversed
between their origins and the point of detection. The amount of matter
traversed then is related to-cosmic ray age. Furthermore the nature of
the charge composition that is deduced to exist in the source region must
9
be directly related to the nature of the source itself and the elemental
building processes that occur therein. This deduced cosmic ray source
composition is different from the solar system composition. Attempts to
explain these results lead to the conclusior that galactic cosmic ray
elements must have had a different origin than solar sysfem elements.
Cosmic rays may have been produced and accelerated in supernova explosions
(Colgate and Johnson, 1960),or are produced in the region around pulsars
and accelerated to high energies by their large magnetic fields (Gold,
1969; Kulsrud et al., 1972)jor are produced and accelerated during the
collapse of a small mass star to a white dwarf (Cowsik, 1971).
The most plausible suggestion for the origin of cosmic rays is that
supernovae represent the dominant source of cosmic rays since: (1) an
enormous amount of energy is released (2) the shook wave imparts large
velocities to the mass in the envelope, and (3) there is a high concen-
tration of heavier elements (Z26) compared to hydrogen and helium which,
during the explosion, are processed to even heavier elements. If this
suggestion is correct one would expect the cosmic ray composition to
reflect advanced stages of nucleosynthesis rather than abundances obtained
under static conditions as would be obtained in the sun since the explo-
sion will alter pre-supernova abundances. By comparing the cosmic ray
composition measured by experiment with that predicted by models of
nucleosynthesis and stellar evolution, after propagational effects on the
composition have been removed, one hopes to confirm or deny the signifi-
cance of specific nucleosynthesis models at the cosmic ray source, and
hence identify the astrophysical site of cosmic ray origin.
Charge composition studies have always suffered to some degree from 1)
lack of charge resolution and 2) counting statistics. As a result of these
10
very basic limitations, the finer details of chemical composition, so
important for theories regarding the origin and propagation of cosmic
radiation, are poorly known, particularly the abundances in the 10 Z 28
charge range. However, with improved charge resolution and increased
counting statistics due to large geometry factor detectors, one should
be able to distinguish charges out to Z - 30 uniquely.
This thesis will report on one aspect of a study undertaken to obtain
the charge composition of primary cosmic radiation from Z = 10 to Z = 28
for energies above 1.16 GeV/nucleon. The charge resolution of the detector
and the total exposure factor represent a useful advance to overcoming
limitations (1) and (2) mentioned previously. In what follows will be
described a charge identification module (CIM) with a large geometry
factor consisting of two plastic scintillators, one inorganic
scintillator (CsI), and one Lucite plastic Cerenkov radiator. The charge
identification module was launched on a balloon flight on 14 November 1970
from Holloman Air Force Base, Alamogordo, New Mexico (320 51.7' N, 106*
7.3' W), as the top module of the High Energy Cosmic Ray Experiment (HECRE)
(See Figure 1) sponsored by the Laboratory for High Energy Astrophysics,
Goddard Space Flight Center, Greenbelt, Maryland. The vertical geomag-
netic cutoff at Holloman AFB is 5.0 GV. (This corresponds to B a 0.93 for
all particles, or 1.5 GeV/nuc). The flight, using a 27 x 106 ft3 balloon,
carried the experiment to an altitude of 7.4 g/cm2 residual atmosphere
(110,000 ft.) where it floated for 16 hours. All systems worked as planned.
The balloon also drifted across the United States to the East Coast, a
change from 4.9 GV cutoff to about 3.25 cutoff at altitude.
This thesis concerns itself with a description of that instrument, the
data received during that flight, its analysis and interpretation, and the
50cm6.4mm PLASTICSCINTILLATOR LUCITE LIGHT
12.7mm UVT LUCITE PIPEHEIGHT CERENKOV COUNTER
IN CM17 (L
S1 SC 1SC 2
30cman SC3O------------------ SC4
-- DIFFUSIONCHAMBER- 6.4mmf PLASTIC SCINTILLATOR
rF----- 3mram CsI(TI) S2-----------------------------
-13PMTI I ___
3mm TUNGSTEN
64mm PLASTIC
-36.1- - - -.. . . . . . . . . . .
P. M.
-6.4mm PLASTICEE MSCINTILLATOR
M.//////////////////27mm IRON
-108-------
IONIZATION SPECTROMETER
Fig. 1. Schematic diagram of the High Energy Cosmic RayExperiment, an ionization spectrometer.
12
implications to be drawn therefrom.
II. DESCRIPTION OF EXPERIMENT
II,A. Charge identification module
II,A. 1. Discussion
The entire High Energy Cosmic Ray Experiment (HECRE) con-
sists of a charge identification module, a trajectory-defining system (a
spark chamber with 4 sets of grids), and a varying number of tungsten
and iron modules used for energy determination. Thus the basic experi-
mental observables of primary cosmic radiation may be measured at one
time in one large detector. This dissertation concerns itself with the
interpretation of the data of the charge identification module (CIM);
therefore, the next few sections will be devoted to describing in detail
this module. Since the data analysis depends quite heavily on informa-
tion gathered by the spark chamber module, it will be described briefly
in a separate section. A schematic of the charge identification module,
consisting of two plastic scintillators, a CsI (TZ) scintillator and a
Lucite Cerenkov radiator, inclusive with the spark chamber grids is shown
in Figure 2.
The CIM was designed to meet the following requirements:
(1) Determine the charge of the incident nucleus to + 0.5 charge units
up to Z = 30
(2) Have a large geometry factor to increase statistics for heavier
nuclei
(3) Determine the trajectory to improve resolution and give path lengths
through the overlying atmosphere.
The two plastic scintillators define the acceptance geometry of 2784
cm2-ster of the system while the cesium iodide and Cerenkov counters are
13
PMT WT M
- - 50 cm .
(SI) 6.4 mm PLASTIC SCINTILLATOR
LUCITE LIGHT PIPE12.7 mm UVT LUCITE
DIFFFUSIONCHAMBER ,
3mm Cs1 (TI)
(S2) 6.4 mm PLASTIC SCINTILLATOR
Fig. 2. Schematic diagram of Charge Identification Module (CIM), the top moduleof the High Energy Cosmic Ray ionization spectrometer experiment.
15
the principle charge-determining elements. This geometry factor, at the
time it was first flown, was two orders of magnitude larger than counter
telescopes commonly flown on balloons and about one order of magnitude
larger than that flown by von Rosenvinge (1969). Comparably-sized geome-
try factors have since been attained by Juliusson et al. (1972) and Smith
et al. (1973).
The pulse height data from the plastic scintillators is also used to
provide a consistency check on the charge determination. These counters
all have dynamic ranges of 104 to cover the charge range from protons to
superheavy nuclei, a factor of 100 in charge or 104 in ionization loss.
The amount of matter in the detector geometry is approximately 5 g/cm2 ;
hence the interaction probability is not excessive and the effects of
nuclear interactions can be corrected with adequate precision. (See Sec-
tion III.G). The CIM weighed about 75 kg and was enclosed in a gondola
pressurized to 1 atmosphere with air. For a more detailed description
of the detector and its operation, consult the references by Ormes et al.
(1968, 1970).
II.A. 2. Coincidence Scintillators
Two plastic scintillators about 30cm apart in coincidence
with one another define the acceptance geometry of 2784 .cm2-ster of the
HECRE. Each 7cintillator detector consists of a square piece, 50 cm x
50 cm x 0.6 cm, of Pilot B scintillator viewed edge on through each of
two opposite sides by an RCA 4524-3" photomultiplier tube which was
bonded to the end of an adiabatic light guide. Note that the maximum
opening angle of the telescope is given by
0max tan -' (/2 x ) = 67* (1)
where 50 cm is the lateral dimension of the scintillators and 30 cm is
their separation. This means that pulses from a given charged particle
can vary by a factor of 2 (1/cos 9max 2) which must be taken into
account in setting thresholds for given particle types and in data anal-
ysis. (See Appendix A. "2. and Section III.B.). Extensive laboratory tests
were conducted on similar pieces before the scintillator final configura-
tion was decided upon. These tests, using sea level muons as & standard
measure of detection, showed that the maximum amplitude response and sharp-
est resolution resulted when the edges of the detector were painted 'ith
NE 560 (Ti02) highly diffusively-reflective white paint and the entire
scintillator wrapped in aluminum foil. Several other configurations were
tried which did not achieve the optimum response and resolution: (1)
wrapping the scintillator completely in diffusively reflective white paper,
which gave both poor response and poor resolution; (2) wrapping the scin-
tillator completely in aluminum foil, which gave the sharpest resolution
but poor response; and (3) painting the scintillator completely with
16
17
diffusively -reflective white paint, which gave the maximum amplitude
response but poor resolution.
Uniformity of response to within + 13% for various positions of
traversal through the large detector area were found to be the case in
general. (See Figure 6 and Section III.C). However, each detector is
unique in production so that individual corrections for corners, weak
scintillation spots, etc. were necessary. A description of how this was
accomplished is given in Section III.C.
A pulse from a coincidence event in the plastic scintillators was
used to trigger the spark chamber. The efficiency of the spark chamber
for registering -a particle trajectory decreases as the delay between
passage of the particle and the application of high voltage on the spark
chamber electrodes exceeds 500 nsec. Plastic scintillators provide the
necessary fast triggering pulse.
Energy loss through ionization is known to be proportional to Z2.
where C = 0.150 ZD gm - I cm2 and I(Z) = 13 .5ZD (B. Rossi, 1952). However,
the light produced by plastic scintillators does not demonstrate this pro-
portionality for all Z, as explained in the next paragraph.
The necessity of obtaining a fast triggering pulse for the spark cham-
ber dictated the choice of plastic scintillators, which are ideal for this
application. But plastic scintillators exhibit a non-linearity of response
of light output with respect to energy loss such that relativistic nuclei
tend to give outputs proportional to Zo (<2) instead of the theoretically
18
expected Z2 . The non-linearity curves for the scintillators used in the
HECRE are shown in Figure 7. The value of the exponent of Z has been found
to be c = 1.64, making resolution of charges in the range 10-30 more
difficult. For iron nuclei this results in a reduction of the signal by
a factor of 3 below the expected value. By way of comparison, Webber
et al. (1973b) find a value for Y of 1.72 for Pilot Y scintillator. (It
is generally known that the light attenuating properties of Pilot Y are
better than Pilot B. These results would indicate that the nonlinearity
of Pilot Y is better than Pilot B).
Final resolution of the top scintillator, Sl, was determined to be
about 17% at charge 10. Although it was not-possible to accurately deter-
mine the resolution at.charge 26 due to limited statistics, indications
were that the resolution was improving as charge increased. For example,
the resolution determined at charge 14, the highest charge with reasonable
statistics, was about 3% improved. An analysis done in section III. F.
indicates that the resolution improved to 8% at charge 26 in this detector.
The implications of this analysis are also given in section III. F. Simi-
larly, the final resolution of the bottom scintillator, S2, was determined
to be about 19% at charge 10 with the analysis indicating it decreased to
10% at charge 26.
The plastic scintillators were each pulse height analyzed to supple-
ment the more linear information from the CsI scintillator. The pulse
height data from the plastic scintillators provided consistency checks for
the other detectors as explained in detail in Section III. F.
II.A. 3. Cerenkov Radiator
This detector consists of a square piece, 50 cm x 50 cm x
1 cm of ultraviolet transmitting (UVT) Lucite viewed by four RCA 4525-5"
photomultiplier tubes, one on each side, which had been bonded to the end
of a UVT adiabatic light guide. Using sea level muons for the standard
measure of pulse height, the Lucite also showed that the maximum amplitude
response and sharpest resolution resulted when the edges of the detector
were painted white and the entire detector wrapped in aluminum foil. Thus
the Cerenkov light is transported by the highly efficient process of total
internal reflection. Four tubes were used on this detector due to the
expected low light level of Cerenkov radiation. Only about 200 useful
photons are produced by a singly charged particle.** Again uniformity of
response over the entire area was found to be within +13%. Corrections
for Cerenkov detector large area variations were also accomplished as out-
lined in Section III. C.
The light output of Cerenkov radiator, in contrast to that of commonly
used scintillators, does not saturate for large values of Z, and instead
is strictly proportional to Za over the entire range of elements. The
following formula is used to compute the energy loss of a charged particle
due to Cerenkov radiation given off by that particle upon traversing a
material in which the velocity of light in the material is less than the
velocity of the particle:
_ 2z C 1] (3)
**These tubes were also specially selected by RCA to have a very low dark
current, 20 nanoamp at 2000 V with a gain of 106, to better separate
signal from noise.
19
20
where d- = energy loss per g/cm 2 of material, B - V - velocity of thedx c
particle, and n = index of refraction = 1.5 for the Lucite used in this
experiment. The validity of this expression over the entire charge range
is of decisiv2 importance in the design because a particle of charge Z is
equivalent to Za independent singly charged particles which have the same
velocity and follow the same trajectory.
Several practical advantages arise from the validity of this equiva-
lence. The relative standard deviation of the pulse height distribution
is proportional to 1/Z; therefore constant resolution can be maintained
between neighboring elements, independent of Z. The combination of a
Cerenkov radiator with scintillation counters thus provides unique charge
identification up to Z z 18, and should provide a resolution of + 1 charge
up to approximately Z ; 30.
The Cerenkov radiation formula indicates that this energy loss is pro-
portional to Z2 and to energy of the incoming particle, through the Ba
dependence. Until the response due to energy of the incoming particle
reaches a plateau, the output can not be used by itself for charge compo-
sition studies since the output is proportional to both charge and energy.
When the response due to energy becomes constant, as it does on the plateau,
then the output response is proportional to the charge-squared. At the low
end of the energy range under study here, this energy dependence property
of Cerenkov radiation limits the resolution of individual charges since
the pulse height distribution is spread out. Minimization of this property
was accomplished by selecting events whose pulse height value was within
0.92 of the relativistic value, since the maximum energy loss per unit path
1length i.e. the plateau is reached when - approaches its minimum value
21
which corresponds to B - 1 for a given n, or relativistic particles.
Another property indicated by the formula is that below some energy
threshold value, no Cerenkov radiation is emitted by the particle. The
threshold energy is reached at [1 - ] 0 which corresponds to - 1,
or B = 0.667 for n = 1.5. This energy threshold property is an advantage
to the experiment since the Cerenkov velocity threshold is used to reject
low energy background particles. These may take the form of slow, heavily
ionizing particles such as large angle alphas which might simulate a high
Z event, or low energy secondary particles which travel upward through the
charge module after being produced in interactions in the spectrometer.
More importantly, the Cerenkov pulse height was used.to reject non-relativ-
istic high Z particles, as explained in more detail in section III. F.
A plastic Lucite Cerenkov radiator such as used in the CIM has an
energy threshold for singly charged particles of 300 MeV and reaches a
plateau in energy after several hundred MeV. Finally, it must be mentioned
that the light output from Cerenkov radiators is very directional. Total
internal reflection techniques are used with plastic radiators to collect
this light, but some light will be lost when the angle of the Cerenkov
light cone exceeds the critical angle for total internal reflection in the
plastic. This also affects the resolution due to the variation in pulse
height of any given charged particle.
Final resolution of the Cerenkov radiation detector was determined to
be about 34%, uniformly to within a few percent, for all charges.
II.A. 4. Cesium Iodide Scintillator
The cesium iodide, thallium-activated scintillator was
assembled as a mosaic of 9 small square crystals each 17 cm on a side in
a large square array 50 cm x 50 cm x 0.3 mm, because these inorganic crys-
tals cannot be "grown" to that size with any uniformity in production.
Since this mosaic had no mechanical strength, the light pipe arrangement,
as applied to the other scintillators, could not be used. Instead a
diffusion chamber technique was employed to view the scintillation light.
The crystal array was placed inside a light-tight box, the inside of which
was completely painted with diffusively-reflecting white paint. Viewing
of this diffusively-reflected scintillation light was accomplished by
four RCA 4525-5" PM tubes, one in each corner of the box. Summing the
four outputs then produced a nearly spatially uniform response.
CsI (TZ) scintillator response is proportional to Z2 over a range of
energy losses, since again ionization losses are proportional to Z2 . In
fact, the response should be proportional to Z2 out to at least Z = 30,
and probably to Z = 40. This makes cesium iodide very desirable for Z = 10
to 30 studies. However, the rise time of the pulse from this material is
approximately 1 psec which necessitated taking special care in the pulse
height analysis to insure no information was lost.
The cesium iodide detector had a final resolution of about 21% over
the entire charge range.
22
II,B.. Spark Chamber Module
For precise charge determination, it is necessary to know the
particle trajectory through the charge identification module. By utili-
zing the direction and position measurements to compensate the pulse
heights for differences in response due to the large opening angle of the
telescope and to variations in light collection efficiencies as a function
of position, resolution comparable to that of much smaller detectors can
be achieved. The 50 cm x 50 cm digitized wire grid.spark chamber, used
for the purpose of trajectory definition, consisted of four independent
sets of X-Y grids of 200 wires spaced about 2.5 mm apart with about 4 mm
between the X-grid and the Y-grid, (thus an X and Y measurement in each
set providing 4 position measurements.) One grid of paiallel wires is
connected to a high voltage buss through ferrite cores, the orthogonal set
being connected to a ground buss. The thin-walled pressure container for
this module added only 0.315 gm cm-2 of matter in the particle path. Upon
receiving a coincidence signal from the scintillators, high voltage is
applied to the sets of grids. The ionization along the track of a charged
particle causes a current to flow in a wire thereby setting its ferrite
core. Later these ferrite cores are interrogated and the coordinate infor-
mation passed on to the digital data handling system. A computer program
was written to translate this information into trajectories which were used
in the data analysis. This is described in sections III. B. and III. C.
Because the detector must be sensitive from electrons and protons up
to iron nuclei, the spark chambers are required to operate over a very
large dynamic range in dE/dx (almost 103). In addition they must operate
in the presence of all the knock-on electrons produced by high Z, high
energy, particles. The spark chambers are operated at the knee in the23
24
efficiency voltage curve, about 2750 volts. This yields a track detection
efficiency of approximately 98% for singly charged minimum-ionizing particles
(sea level muons) with a spatial resolution of + 0.2 cm and an angular
resolution of + 20 for a voltage of 2750V and a gas mixture of 89%-Ne, 9%-
He, 1%-Ethanol. At this voltage between 1.5 and 2 wires were set per
spark. During the flight this spark spreading was found to increase with
Z up to about 3 at Z = 3. Unfortunately, at these large values of spread-
ing an electronic inefficiency develops in the ability to read out the set
cores and so it is not possible to measure the spreading at higher Z
values. This inefficiency results in unset cores within bunches of set
cores and confuses the exact location of the track. In addition, the
knock-on electrons which produce satellite tracks, increase like the square
of the charge. At 1.5 GeV/nuc. approximately 7% of the energy lost by
a particle in crossing the spark chamber goes into electrons with suffi-
cient range to cross all four grids.
The net result of these effects is that as Z increases, an inefficiency
develops in the ability of the algorithms developed for computer analysis
to determine the trajectory. This inefficiency, while greatly complicating
the data analysis, can be determined in principle and so fluxes can be
corrected.(Consult Appendix B).
Because of these difficulties with the spark chamber one must convince
oneself that the detector is giving trajectories correct to within a few
degrees. If satisfactory, then the trajectories can be used to make
corrections of up to 200% to the pulse height values with confidence. In
Figure 3 is plotted a histogram of carbon nuclei at various zenith angles.
This can be seen to agree quite closely with the differential geometry as
25
ZENITH ANGLE DISTRIBUTION OFCARBON NUCLEI
250
200C,
-j
S150 -U-
0
Z
50
-
0 10 20 30 40 50 60 70
ZENITH ANGLEFig. 3. Zenith angle distribution of detected carbon nuclei
(histogram points) compared to the differential geometry
of the Charge Identification Module (solid line) as afunction of zenith angle.
26
a function of zenith angle, except possibly for a slight absence of
particles at large zenith angles. This slight deficit can be understood
in terms of the increased atmospheric absorption of carbon at larger
angles. This good dgreement indicates that the trajectories must be
accurate to within a few degrees.
II.C. Ionization Spectrometer (IS)
For purposes of this experiment, the most straightforward tech-
nique for measuring the energy of primary cosmic rays at high energies is
the ionization spectrometer ("ionization calorimeter") originally proposed
by Grigorov et al. (1958), whereby the incident particle loses its energy
through nuclear interactions in many nuclear mean free paths of condensed
matter. The design of the ionization spectrometer that is described in
the following paragraphs is based on the theory presented by those authors.
The IS consists of two sections: an electron cascade section consist-
ing of twelve tungsten modules and a nucleonic cascade section consisting
of seven iron modules. Each electron cascade module contains a sandwich
structure of one sheet of tungsten 0.32 cm thick followed by a piece of
0.64 cm Pilot Y plastic scintillator which is viewed through air coupling
by a pair of 3" photomultiplier tubes on opposite sides. Therefore each
tungsten sheet is 6 g/cm 2 which is approximately 0.89 radiation lengths
(r.l.) or 0.42 interaction mean free paths. Hence there are about 11 r.l.
in the electron cascade section. Each nucleonic cascade module contains
3 layers of iron 1.25 cm thick interspersed with 3 layers of 0.64 cm thick
plastic scintillator sheets, which are also viewed through air coupling
by a pair of 3" photomultiplier tubes. Therefore each iron module is
66.4 g/cm2 thick which is 0.5 nuclear interaction length or 4.8 r.l. Within
each module the three scintillators are placed to provide a sampling of
the cascade every 1/6 mfp. However, their total light output is viewed
by only 2 PMTs, the outputs of which are added and pulse height analyzed.
The active elements are thus located approximately every 1.6 r.l. of absor-
ber material so as to thoroughly sample electromagnetic cascades, and
every 1/6 nuclear interaction mfp. There are a total of 3.5 nuclear mfp
27
28
in the nucleonic cascade section.
Briefly the IS measures the energy of the incoming particle as
follows. The nuclear interacting particles are incident on the appre-
ciably large mass of condensed matter in tie IS. Through a series of
nuclear interactions the primary particle loses its energy to secondary
particles which are mostly charged and neutral pions. The charged pions
interact further contributing to the development of the nuclear cascade.
The neutral pions decay rapidly into gammas whose energy is dissipated in
electromagnetic cascades. About 60% of the initial kinetic energy is
converted to ionization in this manner. By sampling this ionization at
frequent intervals, it is possible to determine the total primary energy.
The energy of an incoming primary electron is measured through the develop-
ment of the cascade shower in the tungsten modules, where, due to the large
number of radiation lengths for electrons, the cascade develops very rapidly.
In this manner the double-sectioned IS is used to distinguish electrons from
singly charged, nuclear-active particles (mainly protons). Figure 4 illus-
trates the example of the ionization energy loss sampling for an iron nucleus
as identified by the CIM during the flight discussed here. For a discussion
of how the instrument was calibrated for electrons, and protons and heavier
charged particles, consult papers by Whiteside et al. (1973) on the proton
calibration .eat the Brookhaven National Laboratory and Crannell et al. (1973),
on the electron calibration at the Stanford Linear Accelerator Center.
For purposes of this dissertation, where only integral fluxes above the
magnetic rigidity cutoff are presented, the IS was used only to establish
the energy threshold of about 0.5 GeV/nucleon. Differential and integral
spectra over a wide energy range are presented in a series of papers
(Ryan et al., 1972; Balasubrahmanyan and Ormes, 1973; Ormes et al., 1971
29
gS Z=25 l
CERENKOV Z= 27 ± 2
+10
WIRE GRID
CHARGE AND SPARK CHAMBER
TRAJECTORY
DETERMINATION
POSITION IN CM. C8 I Z=24.5t 2
-t10
S2 Z -28.5±2
2 -20
TUNGSTEN 6..
MODULES _____
10
-40
-50 2
ENERGY 2DETERMINATION
- 60
IRON
MODULES
-80
-90
O 100 300 500 700 900
PULSE HEIGHTS IN EQUIVALENT SINGLE PARTICLES
Fig. 4. Schematic diagram of a cascade shower of an iron
nucleus through the ionization spectrometer.
30
and Silverberg et al., 1973).
III. DATA ANALYSIS
III.A. Discussion
The problems of obtaining a high degree of charge resolution
while at the same time collecting a sufficient number of events for good
statistics are connected. The latter requires large area times solid
angle, which means large sensitive areas of counters and unavoidably
introduces variations across the area of scintillation and light collec-
tion efficiency. Large solid angle means variations of emitting path
length of the particle as a function of the angle of incidence, and hence
also variations in light output for different directions. Both effects
tend to reduce charge resolution. The two properties of charge resolution
and a large geometrical factor seem by existing instrumentation to be in
opposition. However by introd-uction of a device such as a spark chamber
for determination of the particle path through the instrument this can be
overcome.
A number of corrections must be made to the raw data from the balloon
flight before it can be placed in usable form and conclusions drawn from
it about propagation and source models, cosmic ray age, and amount of matter
in interstellar space. The ultimate success of the data analysis depends
on the ability of the corrections to separate adjacent charges (i.e., to
improve the resolution) and to distinguish background events. The pulse
height from an individual event may fluctuate from its true value due to
intrinsic statistical fluctuations and detector design fluctuations.
Landau fluctuations and photoelectron statistics fall in the category of
intrinsic statistical fluctuations in pulse height. All geometrical effects
which produce fluctuations in pulse height such as path length or zenith
angle corrections, positional variations due to large size of the detector,
31
32
and nonlinearities of the electronics fall in the category of detector
design fluctuations. The true pulse height for a particular event will
be the convolution of all these factors.
Finally, corrections must be made to the entire set of data for solar
modulation, misidentification of events, and interactions in the detector
which constitute a background.
The next few sections will be devoted to discussing the intrinsic
limitations on resolution, and the size of and corrections for various
geometrical effects. The aim of the analysis is to determine the charge
to within + 1/2 a charge unit up to and including iron so that a resolution
of +4% is required. It is possible that there is an inherent limit to the
resolution. The difficulty of this task is illustrated by the corrections
outlined in the following sections.
III.B. Angle Corrections
III.B. 1. Zenith Angle Compensation
Particle trajectories through the instrument are deter-
mined by using the 4 X-Y position measurements provided by the digitized
wire grid spark chamber. Since all the detectors respond proportionally
to path length through the detector (determined by the zenith angle),this
effect represents the largest correction that must be made. As an example
of the size of this correction, consider a carbon nucleus entering the CIM
at such an angle that sec e 1.20. This charged particle will have the
pulse height of a nitrogen, and could possibly even resemble an oxygen if
the angle is great enough. In the range of Z = 20 to 30, a charge 20 can
look like a charge 28. By utilizing direction measurements to compensate
the pulse heights for differences in response due to the large opening
angle of the CIM telescope (about 600), final resolution comparable to
that of much smaller detectors can be achieved.
A simple sec e correction has been applied to the data since this is
to be expected theoretically. Carbon nuclei have been used to check this
correction since they are the most plentiful and fall in the center of a
range of electronic amplification where no non-linear effects are present.
Pulse heights from the four detectors are selected to include only carbon
nuclei. A two-dimensional histogram is then plotted with the uncorrected
response of the detectors as one variable and zenith angle as the other
coordinate. The variation of pulse height as a function of angle is shown
in Figure 5 for the scintillators and Cerenkov detector. As can be seen
from the figure, sec e is a good representation, within 2%, for the two
plastic scintillators, S1 and S2.
33
2.0 -2.0+ FIT TO CARBON DATA
I.8 - THEORETICAL I.
1.6 I. 6
1.4 SI S 1.4
1.2 1.2
2.0 35>
w J
w 4
I2.08 3.0
+
Jr
I.6 C91 + 2.5
1.4 CERENKOV 2.0
1.2 - 1.5
1.0 - t 4 + - 1.0
0 10 20 30 40 50 60 0 10 20 30 40 50 60 70ZENITH ANGLE
Fig. 5. Relative response of the 4 charge detectors plotted as a function ofzenith angle. Solid line represents theoretical correction (sec G),crosses represent experimental data (carbon nuclei). Note that the scalefor the Cerenkov response curve on the right hand side is different fromthe other 3 detectors.
35
In the case of CsI the agreement is not good beyond 40*. This
discrepancy can be understood in the following manner. The CsI scintill-
ator was placed in a box painted white with photomultiplier tubes at the
four corners. The tubes face the white surface opposite the CsI and
cannot view the scintillation light directly. Light which comes from
a spot near the tubes is collected more efficiently than light from the
center. In fact when the detector response is examined as a function of
area, the center square area is found to produce about 10% less signal than
the average from the other areas. This affects the response as a function
of zenith angle because extreme trajectories cannot pass through the
center. The enhancement at large zenith angles is due to trajectories
which come nearer to photomultiplier tubes and thus produce larger light
pulses. The less extreme trajectories are distributed much more equally
across the area of the detector. In any case, the variation is measured
and can be compensated out.
Angular variations greater than expected have been found in the
Cerenkov detector and are not completely understood. However some ideas.
can be put forth. Below about 150 large light losses at small angles are
caused by attempting to collect the Cerenkov emission by total internal
reflection methods. The Cerenkov cone lies between 450 and 480 to the
particle direction. The angle for total internal reflection is 420 so all
light from vertically incident particles is collected. Between 3* and 60
zenith angles, particles begin to lose some light. Losses increase rapidly
with zenith angle up to about 100 to 150. But at large angles the response
is further enhanced by increased path length through the radiator. Again
the compensations can be measured directly and applied to the data to
obtain useful charge composition information.
III,B. 2. Azimuthal Angle Compensation
The Cerenkov radiator and CsI scintillator were both found
to have azimuthal angle variations large enough to require a correction.
This can probably be attributed to imbalance in gain of the photomulti-
plier tubes. Since four tubes were used on each of these detectors, a
larger gain in any one tube will show up as a significantly larger pulse
height in that tube for charged particles that pass through the detector
near that tube.
The experimental variations were too large for any simple theoretical
fit so an empirical curve was fitted to the data in the following manner.
The scattered data from carbon nuclei were chosen again for the same reason
given in section III.B. 1. A fitting routine on the computer using a 3rd
order polynomidl as the empirical relation, corrected the pulse heights to
their average value. Variations were then reduced to about + 2%.
36
III.C. Area Correction
Variations in light collection efficiencies as a function of
position due to the large physical size of the detector can also be com-
pensated for by using the spark chamber data. The light collection
efficiency F (x,y) is in general a function of two variables:
F(x,y) = g(x) h(y) f(x,y), (4)
a product of a separable part g(x), and h(y) and an inseparable part
f(x,y).
The relative responses as functions of position are plotted in Figure
6 as percentage deviations from the mean for one of the plastic scintill-
ators. The function h(y) varies systematically from -3% near the edges
to +3% in the middle. The variation in x position is quite symmetrical
reflecting good balance in the gain of the photomultiplier tubes. Thus,
the function g(x) is constant within errors. Since the variations in
F(x,y) are somewhat larger than those of g(x) and k(y), f(x,y) must be
comparable to or greater than g and h in certain localized spots. _The
most extreme case is the lower right hand corner which seems to be 6 or 7%
below average.
The area corrections have been made by again fitting a 3rd order poly-
nomial to g(x) and h(y) and applying it to the data. These again are
strictly empirical curves generated to correct the data. Variations in
pulse height due to area position were then reduced to about 3-4%.
37
F(x,y)50
-3 0 +4.5 +3 -4.5X4 0 -
-1.5 -I +4.5 0 0 P0
30 SI
-4.5 - 1.5 +3 0 -3 T20 1
0- 3 + 1.5 +4.5 -3 -6 N
I-10 -
I+1.5 +1.5 +1.5 +1.5 -75
10 20 30 40 50 +10 0 -10Y POSITION g (x)
+10
h(y) Io- I I I
III
-10 I I
Fig. 6. Variations in pulse height as percentage deviations from the meanresponse as a function of position and linear dimension across thearea of the scintillator, SL.
IIID. Nonlinearities of Plastics and PHAS
III.D. 1. Plastics
The nonlinearity of output response of plastic scintillators
to highly charged particles is well documented in the literature (see
Ormes, 1965; Badhwar et al., 1967; where nonlinearities with respect to
carbon output of 20 - 30% have been reported). The response curves of
the telescope elements used in this experiment have been obtained directly
from the experimental data and are shown in Figure 7. The plastic
scintillator S1 is seen to be fairly linear up to Z - 6 after which it
clearly falls below the linear response line. Plastic scintillator, S2,
exhibits a similar response. Measurements of the slopes of Sl and S2
response curves indicate the output to be proportional to (dE/dx)0 's .
This power law correction was applied to the pulse heights to compensate
for this nonlinearity.
Cesium iodide is essentially linear throughout the charge region, thus
confirming it represents an independent linear charge measurement that can
be used in conjunction with Sl and S2.
The poor resolution of the Cerenkov detector, about 35%, made it
difficult to obtain a response curve. The resolution and response data
were obtained using an iterative procedure as follows. Events were iden-
tified from the SI, S2, and CsI data using a 3-dimensional hyperellipsoid.
(See section III.F.). From these results, the individual particle distri-
butions in the Cerenkov detector were unfolded, and the resolution and
response data obtained. This detector is also linear.
39
40
w DETECTOR RESPONSE POINTS100 • , " I ,, I • , , ,
C80 SI S2W 60 /
5 LINEAR -504RESPONSE I
w 30 - -------I SLOPEz.82 SLOPE=.82
20w
w THEORETICAL10 VARESPONSE
100 -w 80 - CER CSIz 60 - 1 -
so 40 -
30 -
20
II
10 20 30 4050 7010010 20 30 4050 70 100w THEORETICAL RESPONSE -
DATA NORMALIZED TO BORON AT 25 x MINIMUM
Fig. 7. Comparison of nonlinear output (points) of the 4charge detector elements to theoretical linear response(solid line) expected for charges 4-9.
III.D. 2. PHAS
Laboratory testing of the electronics circuitry revealed
some non-linearity of output response of the pulse height analyzers with
respect to input for large values of input. This nonlinearity was
measured simply by feeding the electronics a pulse generator output of
the proper shape and amplitude to simulate a photomultiplier tube output
in place of the actual tube output. A polynomial is fitted to the output
response as a function of input, and this polynomial used in a subroutine
of the data analysis computer program to compensate for the deviation
from linearity.
41
III.E. Landau Fluctuations
Pulse height distributions for a given kind of particle of a
given energy in a given detector element are not delta functions. This
results not cnly from geometrical variations in light output and non-
linearities of the detector system, but also results from the fact that
energy loss in a scintillator is a statistical process. The theory
surrounding these fluctuations in energy loss, called Landau fluctuations,
is discussed in the several paragraphs that follow as well as the method
used in overcoming the detrimental effect on charge resolution of these
fluctuations.
The ionization energy lost in a thin detector element by cosmic ray
nuclei of given charge, mass, and energy is not unique; instead a distri-
bution of energy losses results because the energy loss is a statistical
process consisting of many independent interactions between the cosmic ray
nuclei and the bound electrons of the material in the detector element.
The theoretical expression which describes the most probable energy loss,
as taken from the work of Rossi (1952) following the work of Symon (1948),
is presented here:
--------- +__ _ _ (5)
This may be compared to the average energy loss formula given in chapter
II (Eqn. (1)):
S42(6)
42
43
The difference between these 2 expressions occurs primarily in the log
term, which causes the most probable energy loss to become less than the
average loss as B - 1. The distribution approaches its most asymmetrical
form with a large skewness occuring toward high energy losses. This is
due to the increased probability of interactions of the cosmic ray nuclei
with the bound electrons producing large energy transfers to the bound
electrons (the so-called knock-on electrons.) For a given charge, the
effect worsens at higher energies (B 4 1) because the maximum energy
transferred to knock-on's E' = 2 nic 2 (2/1-8) increases (hence the
average energy loss increases), while the most probable energy loss in the
scintillator remains approximately constant.. When the most probable energy
loss is quite a bit less than the average energy loss, the distribution is
highly skewed.
An example of a distribution of energy losses by a singly charged
particle in a scintillator element, called a Landau distribution, is shown
in Figure 8. The distribution in pulse height, which is not symmetric with
respect to its maximum, decreases the charge resolution. For example, a
large statistical fluctuation in energy loss in one detector can cause a
carbon nucleus to appear to be an oxygen nucleus in that detector. The
ability to resolve different charges depends on minimizing the effects on
charge identification of the skewness and the width of the Landau distribu-
tion.
The Landau distribution depends on the parameters X, which determines
the shape of the distribution, A, which determines the width of the distri-
bution, and the most probable energy loss Eo-Ep , which determines the loca-
tion of the peak of the distribution. The quantities X and A and a term j
0.4
LANDAU
) DISTRIBUTIONo-j
0.3
wzwU 0.2
0 I I I I I
-J0.I
0
0-2 -I 0 I 2 3 4 5
MOST PROBABLE ENERGY LOSS (ARBITRARY UNITS)
Fig. 8. Example of a Landau distribution for the most probable energy loss in athin scintillator.
45
in the expression for Eo-Ep are in turn determined from the parameters
G(O,Z) and Ba. Below are presented the formulae for the parameters G and
A discussed in terms of the properties of the cosmic ray nuclei (charge Z,
mass M, velocity 0 = ) and the detector element (average charge ZD,
average mass number AD, thickness X).
G p~ EA (7)
where G = 0.150 ZD. The functions j(G, 2 ), b(G,B2 ), and X(G,B") areAD
graphed in Rossi. The value of X determines the amount of asymmetry of
the distribution: X is largest forsmall values of G which corresponds to
highly relativistic particles. The quantity A has the dimensions of energy
and is a measure of the width of the distribution.
The ultimate resolution of any detector is determined by these statis-
tical fluctuations. Allowing for values of Z different from one, one can
calculate the curve using the method outlined in Rossi. Sample calculations
using the formulae presented previously generated the Landau curves shown
in Figure 9 (calculated with 0 = 0.95 particle in a scintillator element).
The Landau FWHM calculated here refers primarily to distant collisions with
electrons in the scintillator and not to knock-ons from close collisions
which are responsible for the Landau tail. However, the ratio of the aver-
age energy loss to most probable energy loss for minimum ionizing particles
goes from approximately 1.25 for Z = 1 to less than. 1.01 for Z = 20. Hence
the distortion of the Landau tail also decreases significantly with increas-
ing charge.
The dashed line in Figure 9 represents the separation between the
\ (Z+1) 2 _ 2
\ 2 + =.95 > 2.1 GeV/nuc
S7y2 =50 => 5.7 GeV/nuc24 \ = 102 => 8.4 GeV/nuc
\o y= 10 = > 28.7 GeV/nuc20 2 = 104 > 93 GeV/nuc
E 16
12
-J 8
4 -
0 4 8 12 16 20 24 28 32
Fig. 9. The intrinsic resolution due to Landau statistical fluctuations in energy lossas a function of charge, Z, for various energies (solid curves), compared to theresolution required to separate adjacent charges (dashed curve). The curve labelled
= 095 is applicable to the data in this paper.
47
charges while the points represent the full width at half maximum
calculated from Landau distribution for single detectors. Note that at
8.4 GeV/nucleon which is near the mean response for a balloon flight
conducted where the cutoff is 1.36 GeV/nucleon, the FWHM exceeds the
separation for Z > 22. At high energies this problem extends well down
to Z = 16, and is further worsened by the skewness of the distribution
becoming more extreme at higher energies. This is shown in Table 1 where
the probability of a Z = 25 particle simulating the ionization loss of
other charges is given. (For reference purposes, the energy lost by an
iron nucleus of these energies is about 1.3 GeV in a 1/4" plastic scintill-
ator). The first and second lines of the table, which roughly correspond
to the mean energy under study here illustrate that the problem is not
too severe at these energies. The problem arises at higher energies where
the distribution becomes more skewed, making possible an error of identifi-
cation of the charge of 1, 2, or even more charges.
It would appear from this table that the goal of + 0.5 charge units of
resolution is completely unachievable above a few GeV/nucleon. However
the situation is not as bad as it seems at first because fluctuations which
cause the skewness of the Landau distribution are caused by the production
of a few very high energy knock-on electrons. Since these knock-on elec-
trons have sufficient range to carry their energy out of the detector, the
distribution of light produced will not exhibit this extreme skewness. The
tails from the distributions are effectively removed and the problem of
fluctuations exhibited in the table are greatly reduced. However, this
gives rise to another effect. Then a significant fraction of the energy
lost goes into electrons which leave the detector, so that the mean light
output is reduced. The last column in the table shows this effect becomes
Table 1
STATISTICS ON LANDAU DISTRIBUTIONS FOR RELATIVISTIC Z-25 NUCLEI
Energy E(GeV/nu) Y - 2E Et(MeV).* P(<24.5) P(24.5 - 25.5) P(25.5 - 26.5) P(>26.5) fout **
5.7 7.1 50 0.03 0.84 0.13 0 0.8%
8.44 10 10 0.07 0.67 0.19 0.07 3.5%
28.7 31.6 103 0.08 0.48 0.22 0.22 10.4%
93 100 104 0.09 0.40 0.23 0.28 15.5%
*Et is the maximum energy which can be transferred to a single knock-on electron.**f out is the fraction of energy into electrons with range greater than the detector thickness.
49
important for iron at energies above 25 GeV.
Because any single measurement of charge is subject to these statis-
tical fluctuations, multiple measurements using multi-element telescopes
are essential to reduce their effects. Lezniak (1969), using a multi-
detector telescope on Pioneer 8, has shown that improved resolution is
possible with a "minimum of three" technique. He showed that the width
of the energy loss distribution for sea-level muons in solid state detec-
tors is seen to decrease from FWHM = 30% to 22%. He concludes that the
improvement results from diminishing the Landau tail in order to obtain
an energy loss near the most probable energy loss.
Linsley and Herwitz (1956) have given an.excellent qualitative discus-
sion of the influence of Landau fluctuations on the possibilities of
charge determination of cosmic ray particles by means of Cerenkov and
scintillation counters. They find the Gaussian approximation for
relativistic heavy nuclei to be good. Corydon-Petersen and Lund (1969)
have performed Monte Carlo calculations which showed that poor charge
resolution in such counters in general cannot arise from Landau effects.
These calculations confirm that measured pulse height distributions for
higher atomic numbers turn out to be Gaussian in shape, as predicted by
Linsley and Herwitz with a width small compared to the distance between
the mean output from neighboring Z numbers.
The method developed here utilizes four detector outputs to calculate
the characteristic charge type. The most probable event type is calculated
and an average over all detectors is taken. Any extreme fluctuation will
appear as an anomalous pulse height value in only one of the four detectors,
i.e., by demanding consistency between measurements, background events are
eliminated. The methods for charge identification and background elimina-
tion are discussed more fully in the next two sections.
III.F. Four Dimensional Hyper-Ellipsoidal Charge Determination
The first step in the analysis of the data from the flight was
to create a 2-D matrix of scintillator outputs for all events. One of
these 2-D pulse height matrices is shown in Figure 10. The vertical posi-
tion of each charged particle cell in the matrix corresponds to pulse
height in one detector while the horizontal position corresponds to pulse
height in any other detector. Each cell contains a number telling how
many events occurred within the corresponding combination of detector out-
puts. The letters represent numbers greater than 9, starting with A=10,
B=11, etc. These data point clumps, corresponding to particles of a
particular charge value, cluster around a line which to first order is
straight having a slope determined by the ratio of the response in the two
detectors. Since this ratio is very closely 1, the slope is i, and the
line is at 45*. The matrix shown was created using programs on an IBM
360/75 computer.
Because of corrections .in the data analysis to this point, each charge
group stands out as an individual clump of particles in the 2-D matrix of
scintillator outputs. However, due to dispersions in the detectors, the
observed pulse heights are distributed around the centroids characteristic
of the pulse height of the relativistic value (0>0.92) of the energy loss
through ionization of each charge. (The word "relativistic" is underlined
due to its importance for the Cerenkov detector centroid values. The
charge determination is extremely critical because of its coupling with
energy determination. Below about 2 GeV/nuc, the Cerenkov response is
energy dependent and so charge analysis depends upon the energy per nucleon.
However, by requiring the Cerenkov detector pulse height response to be
50
51
6 3 2 ........................... .....................1. a
:a 1 l 1 I 1
6 22 ............................................. ... ... ................... ..... .. ... ..... ............ .. . ,......
. . I l a 12
I .It 2422 ; 21 111As at a t .14 14234 22ss 1
02 :....Z =2 ... ...... . .... . .1 1 . . .2115111 i82 , 22I2 I41 11 2& 3 1
W I I i 12I ,
a• sIl s . 11 I
Z22 1
a . . .. I. s .I I
52 ........................................
522 542 562 582 602 622
CHANNEL NUMBER
. 1; . I 1 I a s1a
1 • 1! .. 13 . I • •
Pulse heights have been corrected for detector depenences but
background events have not been removed.
592 ................ •w. ............ ,,... ...,| . o s I I r Jcl47 |
1.a. ; I 11I 1a 1 21
.e i i 1. 1 t. l* 1 .
1 . .. .
backgroundl events have not been removed.
52
within a certain "distance" from the centroid, or relativistic value, one
can be assured that the events detected are above the vertical geomagnetic
cutoff and not low energy events. (See the following paragraphs for a
fuller discussion). Single- and two-dimensional pulse height distributions
are generated from the corrected pulse heights for each of the four detec-
tors in the CIM, two scintillators (S1 and S2), the Cerenkov detector (C),
and the cesium iodide detector (CsI), i.e. Sl, S2, C, CsI, and pairs Sl
vs S2, S1 vs CsI, S1 vs C, S2 vs Sl, ... etc. From these the centroid of
each charge in each detector and the resolution of each detector were found.
The charge determination procedure may be considered from the follow-
ing point of view. An N-detector system forms an orthogonal space of N-
dimensions, in which each axis is the detector output.in units of the
resolution of the detector, cij, defined by
C. a. __ (8)
where Cij is the centroid and Rij is the resolution for the ith chargein
the jth detector. In this hyper-space the ith centroid is located at the
point (Cil/ail, ... , Cij/aij , ... CiN/oiN) and a given event is located at
the point (Pil/oil, -" Pij/oij ..., PiN/iN), Pij is the observed pulse
height of the ith charge in the jth detector and N is the total number of
detectors. (For each event, the data consists of N=4 measurements.) The
value of 'i' is chosen such that Di, the total distance, is a minimum where
= __ (9)
This 'i' value is then assigned to that event as the charge to which the
event was closest (i = 10, ..., 28). Particles were said to have inter-
acted, or are background, if they lay outside of the 4-D hyperellipsoid.
53
In order to demonstrate the selectivity of the method, a 1-dimensional
charge distribution was reconstructed. The charge is determined as the
minimum in the parabola formed by the distances to the three closest
centroids. In this method, neither the distances nor the determined
charge value are integers. The charge value is assigned to the closest
integer value which the determined value approached. Both the sagitta of
the parabola and the minimum of the parameter D1 can be used as measures
of the error.
Charge identification accuracy is a = + 0.51 at magnesium and increases
about linearly up to a = + 0.66 at iron. These total errors, which are
determined by the charge identification routine, may be compared to the
total*error calculated from the resolution of each individual detector
element:
S + . + (10)
At charge 12 where the resolution, and hence a, for each detector -is known,
this calculation yields a = 0.50 in excellent agreement with the value
given above. Reversing the calculation can yield the approximate resolu-
tion at charge 26 for detectors Sl and S2 where it is not known. First
assume that the resolution improves in both detectors in about the same
ratio. Using a resolution of 34% for the Cerenkov detector, 21% for the
cesium iodide detector, and 6% total resolution (a = 0.66) at charge 26
yields a resolution of 8% for Sl and 10% for S2, which is not unreasonable
considering the resolution had improved by a few percent at charge 14 in
both detectors. The implications of this resolution are as follows. The
final resolution of a given detector d is calculated from
54
q + + O(11)
where L stands for Landau statistics, ph for photoelectron statistics, and
sp for the spatial resolution. The Landau resolution at charge 26 is
about 3% (see Figure 9) and the resolution due to photoelectron statistics
is less than 1% (at Z=l photoelectron statistics are about 18%: they
decrease as 1/Z). The spatial resolution is then deduced to be about 5-6%
in agreement with sections III.B. and III.C. (angular resolution about
2%, area resolution 3-4%). This indicates detectors Si and S2 are still
dominated by spatial resolution. If this number could be reduced to 1%,
the results of future flights of this detector would be significantly
improved. Since the cesium iodide detector is also an ionization energy
loss detector, the same analysis can be applied to it. The constant total
resolution of this detector is a clue that the spatial resolution was very
poor, probably due to inefficiency in the collection of light photons in
the large diffusion chamber. Landau statistics are not a part of the
calculation for the Cerenkov radiator since Landau fluctuations apply only
to ionization energy loss processes. Photoelectron statistics can account
for at most 7% of the final resolution of this detector. The Cerenkov
response was determined to be such a complicated function of azimuthal
and zenith angle, and position within the large area of the detector that
it is felt that the limit to the resolution is reached due to uncertainties
in the spatial correction rather than photoelectron statistics or other
causes. Hence in every detector, it would appear that the spatial resolu-
tion limits the final resolution achieved in that detector, which in turn
55
limits the total resolution achieved by the multidimensional charge iden-
tification routine.
However individual charges are reasonably well resolved with back-
ground rejection quite effective as can be seen in the final charge histo-
gram shown in Figure 11, where the peak-to-valley and charge resolution
are good. It would appear from Figure 11 that odd charges have not been
resolved. It must be remembered that the computer algorithm works with
the pulse heights from all 4 detectors to determine a non-integer charge
value for each event. The charge histogram shown in this figure is
constructed from the non-integer charge values of 2 detectors, Sl and S2,
only; hence the resolution does not appear to separate charges uniquely.
The algorithm also assigns an integer charge value to an event based on
whether the non-integer charge value lies within the hyperellipsoid defined
for that charge. Using this method, there is no difficulty assigning a
charge value as either odd or even. Therefore odd charges are determined
usually as well as even charges over the entire charge range.
Any good events lost in this selection procedure have probably been
incorrectly identified as background. Correction for the rejected good
events will be discussed in the section on background that follows.
200180 = 12
180FWHM=10% Z= 10-26
160 Z14 TOTAL NO. OF EVENTS =4628
140
z 120LU
w 100
o 80 - FWHM =6%
Xr Z=26W 60Z=16
z 40 - Z Z= 20 Z=22 Z=2420 J'L Z= 18 4 J200
50 60 70 80 90 100 110 120 130 140 150 160 170
BIN NUMBER
Fig. 11. Charge histogram, Z = 10-26, taken from two dimensional matrix, S1-S2,of corrected pulse heights with background removed.
III.G. Background Correction
Selection of "single" events, as determined using the criteria
outlined in Appendix B on the spark chamber tracks, served to eliminate a
large fraction of background events. As d7iscussed there, the spark chamber
helps to discriminate against multiple particle background events, such as
atmospheric showers, since a unique track can not be found. The presence
of the Cerenkov detector, with its energy threshold, makes the rejection
of low energy background, both in the atmosphere and from interactions in
the spectrometer, much easier.
Nuclear interactions and other anomalous events are also discarded by
demanding consistency of the charge determination between the elements of
the CIM. Each charge is defined in a very localized region in 4-D pulse
height space. It is assumed that most background particles do not lie in
the expected regions of the 4-D hyper-space, i.e., these events should be
interspersed between and scattered about the clumping. Since background
events are uniformly distributed over a much greater volume, background
subtraction becomes straightforward by demanding consistency between the
charge values determined in the 4 detector elements.
As discussed in the previous section, the charge value (non-integer)
is determined as the minimum in the parabola formed by the distance to
the three closest charge values. The charge is assigned to the closest
integer value which the determined value approached. Another parameter
is defined for all 4 detectors as the sum of the squares of the distances
of the non-integer charge value from the integer charge in units of the
resolution in each detector. Particles were said to have interacted, or
are background, if they lay outside of the 4-D hyperellipsoid with semi-
57
58
axes defined by the value of this parameter such that applying this
criterion yields an L/M ratio and individual charge composition up to
Z = 10 that agrees with the published literature. Figure 12 shows the
same computer matrix printout of the raw data of Figure 10 after back-
ground has been removed by applying the four dimensional hyperellip-
soidal charge determination computer algorithm. (This matrix output is also
used to plot the charge histogram of Figure 11).
In order to insure that background is minimized, the strict criteria
on track determination, energy determination and charge determination
discussed in the previous 2 paragraphs have been placed on every event.
However this may mean that some good events are discarded. for example,
the high efficiency of the spark chamber for singly charged particles has
made the spark chamber sensitive to knock-on electrons produced by high Z
nuclei and to Compton electrons from y-rays coming from the spectrometer.
As a result, the VH nuclei tracks have been confused by the presence of
background. Or, for example, a good event may interact near the top of the
energy spectrometer producing backscatter through the CIM. Anomalous
pulse heights from the backscatter would cause the event to be rejected due
to inconsistent pulse heights in the four detectors.
It is possible, and necessary, to make a correction for good events
that are identified as background, and as such are removed from the charge
distribution. For the charge determination procedure, events which lie
outside the pulse height error range, but which have simple tracks as
defined by the spark chamber, represent at most a 15% correction to the
data. Background events of this type were most abundant at lithium and
fell off rapidly with increasing charge so that heavy nuclei should not
59
632: ... ....
622 ........................................................... ......
2-=.1 -2 12 2
2 2 1222 1222222 122 22
S212 1 * 221 1 2
111 2 11 1 1 2 22:2 12222
S 2 2 3 3 2 2 * 2s .2
Z- .222222 . ....
= =22 2
12+ '1 . 2.2.
5 92 : ......... ....... . .. ..... . ... . .. .............. 2.. .... 2 ... .2 2112 1 2 11
2222 . 11. . 111
Z= 20- 2 1
S. 22222I 2 1 11
S 5 7 2 :............................ . ...............
2 22 2 .2i I2 .t
552 .-- il 12 2
12 2• 1 1 1 e s1 1
2 ,1 1222 . t 2
* 222252C51 12 221 2 2
552.. ..........................................
2i 1 11 1 .11 1
2 221't 1 2
5 3 2 ........................ ......... ......... ........ . . . ...................... ......
2 2 2------- 2- ^---- -
522.................................. ...............
522 542 562 582 602 622
CHANNEL NUMBER
Fig. 12. Two dimensional pulse height matrix, scintillatorsSi and S2, with background events removed.
Fig. 12. Two dimena2sioa ple egh ati cntlatrS1 and SJ1 ithbcgoudeetsrmvd
60
have been affected much. To check that the spark chamber track classi-
fication scheme was not itself biasing the data, all complex events, i.e.
those which do not satisfy the criteria in Appendix B, were subjected to
the same charge determination procedure as used on simple events by
assuming these complex events had trajectories at the most probable
response angle of the coincidence scintillators. The data was consistent
with being background. The most probable correction of 5-10% can be put
on losses of well identified complex events.
The background measurement can be compared with an estimate of the
fraction of events that will interact in the detector as follows. One
would expect a correction factor of the form.ex/A where x is the mean thick-
ness of the detector in g/cma and A is the mean free path for absorption.
The interaction mean free path in a compound material, Xic is given by
(12)
where Xij is the mean free path for an ith incident nucleus on the jth
component nucleus with Pj the partial weight for the jth nucleus. The
quantity Xij is calculated from Aij = Al where n is the number of jn
nuclei per gram of j element and Aij is the black disc formula for the
absorption mean free path
.Ai (13)
where Ai and A are the atomic number of the cosmic ray and target nucleus,
and mj and rj are the mass and radius of a nucleon. This can be simpli-
fied by considering an upper limit to the cross section for interaction
oij = 1/Aij and letting the target nucleus be hydrogen. Thus A = 1,
61
mj - 1, rj 1.45 x 10-13 cm. The mean free path then calculated will be
a lower limit to the true mean free path.
The mean free paths in plastic, CsI, and aluminum have been calculated
for magnesium, sulphur, calcium and iron as listed in Table 2. For the
plastic calculation it is assumed that there are equal numbers of hydrogen
and carbon atoms per molecule. The detector material in the telescope
consisted of 2.78 g/cm2 of plastic, 1.43 g/cma of CsI, and 0.86 g/cma of
aluminum, a total of 5.08 g/cm 2 of material in the detector geometry.
Using these numbers, an upper limit of 32% for nuclear interactions
of iron cosmic rays in the detector material is estimated. (It is inter-
esting to note that the number of iron group.nuclei identified as having
complex tracks is consistent with the expected number of interactions of
iron group nuclei in the CIM.) In addition background is expected from
large statistical fluctuations in the pulse heights and from interactions
in the matter surrounding the detector. Hence the correction factors used
of 1.32 for the LH group, 1.36 for the MH group, and 1.47 for the VH group
are in reasonably good agreement assuming most interactions occur in the
detector material.
62
Table 2
INTERACTION MEAN FREE PATHSIN PLASTIC, CESIUM IODIDE, AND ALUMINUM (g/cm2 )
Plastic CsI Aluminum
Magnesium 12.64 103.43 19.61
Sulphur 11.31 96.27 17.81
Calcium 10.35 90.79 16.47
Iron 9.00 80.88 14.57
III,H. Correction for Overlying Atmosphere
Before one can interpret the measurements of the charge compo-
sition at balloon altitudes in terms of the extraterrestrial abundance of
these nuclei, corrections must be made for production and loss in the
atmosphere. When the primary cosmic ray beam passes through the upper
layers of the atmosphere, the overlying material has a 2-fold effect on
the measured 4.ntensities of the nuclei at a particular charge. Firstly,
some nuclei will interact and be removed from consideration completely,
and secondly, nuclei will interact and give rise to fragments of lighter
charge which will still be in the charge range under consideration. The
correction in general requires a complete knowledge of the fragmentation
parameters of various elements into lighter nuclei. In practice measure-
ments of the absorption of each cosmic ray element in the upper atmosphere
are used to make these corrections (Webber and Ormes, 1967). For reason-
ably accurate results, the latter method requires large statistics for
individual charges which are difficult to collect, since the flux of high
energy cosmic rays is low and most balloons rise rather quickly to float
altitude. Therefore the first method will be used to find the charge
composition at zero depth. The second method, however, has been used to
correct the integral flux measurements of charge groups since this is well
within the associated errors.
The most straightforward way of making the atmospheric correction to
integral fluxes of charge groups is to observe the variation of fluxes
of the various nuclei as a function of depth and extrapolate that data to
the top of the atmosphere. This is done by obtaining the absorption mean
free paths from a plot of flux versus depth. The data on fluxes presented
63
64
here are corrected to the top of the atmosphere in just that manner: by
using direct measurements of the atmospheric absorption of the various
charge components.
Taking advantage of the large geometriual factor the atmospheric
attenuation mfp of nuclei groups 105Z14, 15 Z 19, 20 Z 23, 24 Z 30,
15 Z 23, and 20 Z 30 have been measured with increased statistics using
data from both the ascent and descent portions of the balloon flight.
(This flight provided a unique opportunity for measuring the mfp in air.
The experiment not only ascended slowly but, due to a failure of the experi-
ment cut-down mechanism,descended slowly to the ground from altitude
as the balloon gradually lost lift, instead of parachuting to the ground.)
FZom radar and barometer measurements, the altitude-time profile for
both ascent and descent are known. The data is divided into 5 g/cm 2
intervals and the fluxes of the different charge components are calculated
in each of 10 depth intervals over the range 5.0x 55.0 g/cm 2 . The,thick-
ness of atmosphere penetrated by each incident particle is determined from
its trajectory through the detector and the altitude of the balloon at the
time of its arrival; thus particles penetrating any given thickness of
atmosphere were observed from various zenith angles at various balloon
altitudes. The effective (area) x (solid angle) x (time) factor for each
depth interval is calculated by numerical integration of the detector's
differential geometrical factor over the trajectories (Monte Carlo tech-
nique, see Crannell and Ormes, 1971).
Figure 13 shows the depth dependence of the fluxes of charge groups
105Z:14, 15 Z 19, 20 Z 23, and 24<Z530 above 1.16 GeV/nuc along with the
results of a linear least squares fits. Data points have been plotted at
65
100
Z= 10-14 Z= 15-19
38.5 5.2
10-10 32.4*±8.7
x-2
1> I0 - -
- 2 =20-23 I Z=24-3016.8±2.7w 23.7±5.9-
10- 2
-3
10 20 30 40 50 60 10 20 30 40 50 60
DEPTH (G/CM2 )
Fig. 13. Relative flux of charge groups as a function of depth inthe atmosphere. The slope of the least squares fit to the
data (solid line) yields the atmospheric attenuation mean free
path.
66
the mean atmospheric depth traversed within each depth interval. Effects
due to the variation of geomagnetic cutoff with incident direction are
negligible because each data point represents an average over all azimuths
and a wide range of zenith angles. Correction for energy loss through
ionization in the atmospherehas been neglected. For example, the energy
loss through ionization in air for iron nuclei is about 350 MeV/nuc in
7.4 g/cm2
The fit of the data yields atmospheric attenuation mfp for the differ-
ent charge groups as listed in Table 3a, where they are compared to other
experimental results. The values are seen to be in generally good agree-
ment with other results. The results for charge groups 15:Z 19 and
20 Z 23 represent the first direct measurements of the atmospheric atten-
uation mfp. These values may be compared to the Webber et al. (1972)
summary of the experimental data in emulsions of Cleghorn, (1967), and the
direct measurements in air of Webber and Ormes (1967) and von Rosenvinge
(1969). Although no error bars on the values were published by Webber
in the summary paper, there still appears to be systematic differences
between those values and the values measured by this experiment. The
measurements of Webber and Ormes (1967) were made at lower energies where
energy loss through ionization in air can not be neglected. Waddington
(1969) pointed out that this correction to the mean free paths appears to
have been done incorrectly. It also appears from the table as though one
can not simply extrapolate the results of emulsion experiments to air. All
emulsion measurements appear to be about 20% too low. The results of
Mewaldt et al. (1971) are statistically the most significant so any com-
parison should be weighted toward these measurements. It can be seen that
Table 3a
ATMOSPHERIC ATTENUATION MEAN FREE PATHS (g/cm2 )
Charge Present Experiment* Mewaldt Webber Freier & von Rosenvinge Cleghorn,Group et al.,1971* et al.1972+,** Waddington, et al.,1969a,b** 1967**
1968c**
10sZ&14 38.5 + 5.2 28.1 30.0
15 Z19 32.4 + 8.7 25.0 22.5
20,Z,23 23.7 + 5.9 22.1 19.1
24,Z,30 16.8 + 2.7 15.8
15,Z,23 28.4 + 5.4 22.4
20,Z,30 19.5 + 2.8 19.7 + 1.6 16.1 16.2 16.5 21.9
Z=26 15.6 + 2.2
+Values calculated for groups using mfp weighted by relative abundances.*Measured in air directly
**Extrapolated from emulsion measurements
68
Table 3b
ABSORPTION MEAN FREE PATHS IN AIR (g/cm 2)
Charge MFP
26 16.8
25 17.9
24 19.1
23 20.2
22 21.4
21 22.5
20 23.7
19 25.8
18 28.0
17 30.2
16 32.4
15 34.0
14 35.5
13 37.0
12 38.5
11 40.0
10 41.5
69
the VH group values agree very well. The value for iron, from Mewaldt
agrees quite well with the value found here for the iron group, of which iron
is the dominant member. In fact the value found here is somewhat larger,
which it should be, since the group members, manganese and chromium, will
tend to increase the value over the value for iron. (The group members
Z>26 are so small in number compared to Z = 24-25 that they should not
influence the mean free path value very much).
The integral fluxes of charge groups have been corrected in this manner
in Table 4 in section IV. A.: the graphs of flux versus depth for each
charge group were extrapolated directly to the top of the atmosphere.
Correction factors from this method are given in column 3 of Table 4.
The first method for correction for the absorption-fragmentation
process can be treated in terms of solving the one dimensional diffusion
process. The number of nuclei at depth x, Ni(x),is given by the number at
the top of the atmosphere Ni(O), multiplied by a function which involves
all the relevant abundance and nuclear parameters. In this approach it is
necessary to measure values for the abundances of nuclei, and to adopt
values for the relative number of light fragments produced in each inter-
action of a heavier nucleus with atmospheric nuclei, i.e. the fragmentation
probabilities and the interaction or absorption mean free paths (mfp).
Furthermore, one must make the simplifying assumptions that no energy is
lost by ionization and that fragments always maintain the direction of
motion of the primary nucleus. Then the diffusion equation reads
70
where i = 1 corresponds to iron nuclei and i = 17 corresponds to charge
10, neon.
The number of primary nuclei with charges greater than iron is about
10- s as large as that for the iron group (Fowler et al., 1967). Therefore,
it is satisfactory to neglect the correction for nuclei fed into the iron
peak from the SVH group (Z 30), and to adjust for only those nuclei which
leave the iron peak. (Hence the sum in --the equation runs for j<i). Then
for the iron nuclei, the number N(O) at depth x = 0 (top of atmosphere)
is given by
N1 (0) = N(x) exp (+x/A 1) (15)
where A1 is the absorption mfp of iron nuclei. For those nuclei of the
next lighter charge, the solution to the diffusion equation becomes
-I, .A,
A similar solution must also be generated for each succeeding nucleus,
solutions which become even more complex in analytic form.
These equations show that in order to calculate primary abundances it
is necessary to know the mean free paths (mfp) and fragmentation probabil-
ities applicable to the atmosphere. These values are not well known and
appear subject to some controversy. Interaction mfp and fragmentation
probabilities may be measured directly in media such as carbon, Teflon,
or nuclear emulsion that resemble air in their nuclear makeup. From these
measurements estimates of the appropriate mfp in air may be made. (See,
for example, Judek and van Heerden, 1966; Cleghorn, 1967; Cleghorn et al.,
1968; and Long, 1968). These authors found that the fragmentation proba-
bilities are constant with energy in photographic emulsions, and have
71
assumed the same to be true for interactions in air. Direct experimental
determinations of the fragmentation cross sections using protons incident
on high Z material targets have shown that cross sections are constant to
+10% beyond about 1 GeV/nuc. Though all fragmentation interactions have
not been studied completely, variations of cross section with energy above
1 GeV/nuc.seem unlikely. For a summary of results and discussion, see
Shapiro et al. (1971).
The absorption mean free paths (mfp) for individual nuclei were cre-
ated from the measured group absorption mean free paths by assuming that
the measured value corresponds to the most abundant charge in that group
and linearly interpolating between measured values for the amfp to get the
amfp for each individual charge in that group. This method yields the
absorption mean free paths in air for charges 10-26 as shown in Table 3b.
Constructing the individual amfp from the group amfp in this manner does
not increase the error in the final results since each individual amfp is
within the 20% error bar of the amfp for the group to which it belongs.
These errors are included in errors for the final results.
The fragmentation probabilities for air have been created from the
Silberberg and Tsao (1973) nuclear interaction cross sections in hydrogen
(see Table 7) using a correction factor for air based on the latest result:
of heavy ion experiment performed on the Lawrence Berkeley Laboratory
accelerator by Heckman and Greiner.(See Heckman et al., 1972; D. E. Greine:
1973; H. H. Heckman, 1973; and H. H. Heckman, private communication*).
*The author wishes to thank Dr. H. H. Heckman for providing his valuable
results to this author prior-to publication.
72
The correction is calculated as follows. Heckman et al. have found that
athigh energy the cross section for production of element X from projec-
tile C with target B fits the functional form
x xOCB YC'B (17)
where ocx is the cross section, which is separable (factorization) intoCB
a part that depends on the projectile and product yC, and yB' a part which
depends exclusively on the target. From their experiments, YB = AB." ss a
result which is somewhat less than considering the target's cross section
to vary as the geometric area, in which case the cross section would vary
as A2/3 , and also surprisingly less than considering the cross section to
vary as the circumference, in which case the.cross section would vary as
Al /. (This latter case implies the interaction occurs with only an annu-
lar ring of nucleons in the target). Knowing the hydrogen cross sections,
H, to a reasonable accuracy of 10-20%, it is then a simple matter to
correct these for interactions in air. For simplicity of demonstration,
assume air is pure nitrogen, N. Then
_ _ ( (18)
X X
so oCN = (14) " s6 aCH. That is, the cross sections for hydrogen are
multiplied by (14). e56 . In actual fact the calculated correction factor
was based on an air mixture of 80% -N and 20% -0.
This paper utilizes these new results to extrapolate individual charge
composition data collected at balloon depth to the top of the atmosphere.
Previous investigators claiming individual charge resolution at balloon
depth and a'-ain at the top of the atmosphere have nonetheless extrapolated
73
their individual charge composition results to the top of the atmosphere
by lumping their individually measured charges into groups, using group
fragmentation parameters, and redistributing the growth or diminution of
that group back to individual elements.
The results of the present method are given in column 5 of Table 6.
III.I. Correction for-Solar Modulation
Solar modulation introduces another complication to the data
analysis. Its influence on intensity measurements is considerable since
the data under study here was collected at solar maximum conditions. This
influence will be eliminated as much as possible by using the method out-
lined in Appendix C.
The charge intensities presented in column 2 of Table 4 represent those
that would be measured at the top of the atmosphere. The force field solu-
tion is used to correct these intensity measurements:
E(rE) _. -E (19)
where jt (r,E) is the intensity measured at Earth at time t, jo (m~ E+§)
is the intensity in interstellar space, E is the total energy of the parti-
cle, Eo is the particle rest energy, and § is the mean energy loss due to
adiabatic deceleration.
Previous attempts to correct for solar modulation adjusted the measured
intensities to the solar minimum of 1965 using regression curves because
the amount of modulation at solar minimum was unknown (Mewaldt, 1971; von
Rosenvinge, 1969). In order to more reasonably compare the present data to
these past results, this author will also correct the data presented here
to the solar minimum of 1965, but using values given below for the
parameters. Hence, the correction factors, given by the quantity in square
brackets in the equation below, for R=4.9 GV and R=3.25 GV are calculated
using the appropriate parameters from
74
75
L- 4
Urch and Gleeson (1972) have determined the values of for the years
1965-1970 for various values of kinetic energies of helium cosmic rays.
For 1970: = 0.445 GeV/nuc.at T = 1.58 GeV/nuc.(4.9GV); I = 0.425 GeV/nuc.
at T = 0.870 GeV/nuc,.(3.25GV). For 1965: = 0.175 GeV/nuc.for both T =
1.58 GeV/nuc.and T = 0.870 GeV/nuc. (See Figure 7 in that paper). The
solar modulation correction factors are given in column 3 of Table 4.
An important point to remember-is that the charge composition, which is
the main thrust of this paper, is not affected by solar modulation: solar
modulation depends on the Z/A ratio, as indicated in Appendix C, which is
approximately 2 for all heavy cosmic ray nuclei. The Z/A ratio enters the
theory through the quantity I which is defined by
Z (21)
where c represents the force field potential. Approximating the Z/A
ratio to 2 introduces a small error of about 4% in the relative charge
composition, an error which is much smaller than other errors associated
with the charge composition measurements. This error will be neglected in
the charge composition results. Any interpretations about the relative
charge composition are not altered by this approximation. See Appendix C
for a more complete discussion.
IV. RESULTS
IV.A. Fluxes at Top of Atmosphere
Table 4 summarizes the results of this experiment regarding the
integral fluxes measured above the vertical cutoff rigidity at the regions
of ascent and descnt of the balloon and the correction factor calculated
from the discussion in sections III.A. to III.I. This table presents the
data for charge groups Z=10 - 14 (LH), Z=15 - 19 (MH), Z=20 - 30 (VH), and
groups Z=15 - 23, Z=20 - 23, and Z=24 - 30 (Fe).
The resulting fluxes are compared with those reported by other workers
in Table 5. The data chosen for comparison in Table 5 have been chosen
because they represent the most statistically significant data in the
present charge and energy range published to date. [Some workers have
reported their results for integral rigidity spectra and others for integral
kinetic energy spectra. For comparison, using A/Z = 2.10 for charges
Z-10 - 30, a rigidity of 3.25 GV equals 0.870 GeV/nuc.and a rigidity of
4.9 GV equals 1.58 GeV/nuc.] It can be seen from the many data of other
workers that is missing that this survey represents one of the most com-
plete surveys available.
To give the reader an idea of the statistical significance of the
results reported here, the results of Webber and Ormes (1967) are reported
on about 300 nuclei with Z 10, the results of Bhatia et al. (1970) on
440 nuclei with Z = 10 - 28, the results of Freier and Waddington (1968a)
on 315 nuclei with Z 20, and the results of von Rosenvinge (1969) on
about 600 nuclei Z = 10 - 28.
The surveys that are statistically comparable are those of Smith et al.
(1973) with about 1800 total events Z - 10, Mewaldt et al. (1971) with
about 16000 events for Z Z 20, Webber et al. (1973) with about 4000 events
10 : Z 5 28, and Balasubrahmanyan and Ormes (1973a) on about 770 nuclei76
77
10 Z 28. (The integral values quoted for this experiment differ from
the Balasubrahmanyan and Ormes results even though the results are taken
from the same flight of the same experiment. This can be explained as
follows. The integral flux values quoted here a'e taken from ascent which
occurred at 4.9 GV rigidity: 4.9 GV is the vertical geomagnetic cutoff.
The Balasubrahmanyan and Ormes result is taken from an energy measurement
in the ionization spectrometer and converted to rigidity. The results do
agree within errors.) The total number of events detected by this experi-
ment was about 5000 for Z 10. It can be seen that discrepancies exist
among these published results, the value from this experiment being in
general about 20-30% lower where they can be compared.
There are several possible systematic errors which might explain the
discrepancies. In this experiment there is some uncertainty in the correc-
tion for events that are lost due to strict criteria on charge identification.
The systematic effects of uncertainty in collection time or geometrical
factor, or the systematic effects of inefficiency of operation of the spark
chamber for higher charges influence the results quoted here.
Difficulties in comparison of various results may be due to the
various levels of solar modulation prevailing at the time of each experi-
menter's measurements. Both charge resolution and statistics of total
number of events measured by the experiments span a wide range. Some
small difficulties in comparison arise due to non-uniformity in the defi-
nition of the various charge groups. For example, some experimenters
define LH nuclei as charges 10 to 15 while others define this charge group
as 10 to 14. Difficulties in comparison also arise due to the variety of
energy or rigidity cutoffs quoted by other experimenters. And lastly, the
various experiments all have flown under different amounts of atmosphere,
78
from 2 to 7.4 g.cm2 of air, requiring different atmospheric corrections
to be applied to the data. In view of all these differences, the agree-
ment of the flux values amongst various experimenters is generally good.
The discussion of the charge composition data, presented in the next
section, should not be adversely affected by these systematic flux
problems.
Table 4a
INTEGRAL FLUXES** (particles/me ster sec)
Charge Observed Correction Corrected
Group Flux (>3.25 GV) factors.* Flux (>3.25 GV)
-1010-14 (LH) 7.58 + 0.65 x 10- (1.15) (1.32) (1.34) 1.54 + 0.13 x 100
15-19 (MH) 1.59 + 0.32 x 10-1 (1.0) (1.36) (1.34) 2.90 + 0.58 x 10-1
20-23 1.15 + 0.28 x- 10 -' (1.0) (1.36) (1.34) 2.10 + 0.51 x 10-1
24-28 (Fe Group) 1.83 + 0.38 x 10-1 (1.0) (1.47) (1.34) 3.60 + 0.75 x 1 0 -1
15-23 2.64 + 0.41 x 10-1 (1.0) (1.36) (1.34) 4.81 + 0.75 x 10-1
20-28 (VH) 2.93 + 0.46 x 10-1 (1.0) (1.47) (1.34) 5.77 + 0.91 x 10-1
** The fluxes presented here have been corrected to the top of the atmosphereusing extrapolation of the atmospheric attenuation curves.
* (correction for events outside identification) (correction for interactions
in CIM) (correction for solar modulation+)
+ This correction factor normalizes the flux values to solar minimum, 1965,Mt. Washington neutron monitor = 2400 for easier comparison to otherpublished results.
Table 4b
INTEGRAL FLUXES** (particles/m2 ster sec)
Charge Observed Correction Corrected
Group Flux (>4.9 GV) factors * Flux (>4.9 GV)
10-14 (LH) 5.09 + 0.37 x10-1 (1.15) (1.32) (1.24) 9.58 + 0.70 x10-1
15-19 (MH) 1.07 + 0.17 x10-1 (1.0) (1.36) (1.24) 1.80 + 0.29 x10- 1
20-23 6.84 + 1.54 x10- 2 (1.0) (1.36) (1.24) 1.15 + 0.26 x10-1
24-28 (Fe Group) 1.30 + 0.24 x10-1 (1.0) (1.47) (1.24) 2.37 + 0.44 x10- 1
15-23 1.70 + 0.22 x10- 1 (1.0) (1.36) (1.24) 2.87 + 0.37 x10- 1
20-28 (VH) 1.92 + 0.27 x10-1 (1.0) (1.47) (1.24) 3.50 + 0.49 x10- 1
** The fluxes presented here have been corrected to the top of the atmosphereusing extrapolation of the atmospheric attenuation curves.
* (correction for events outside identification) (correction for interactionsin CIM) (correction for solar modulation+)
+ This correction factor normalizes the flux values to solar minimum, 1965,Mt. Washington neutron monitor = 2400 for easier 'comparison to other published
results.
Table 5a
INTEGRAL FLUXES (particles/m2 ster sec)
Charge Present Webber et al., Bhatia et al., Webber & Ormes,
Group Experiment 1973 1970 1967
(>3.25 GV) (->0.85 GeV/nuc) (>1.0 GeV/nuc) (>3.25 GV)
10 < Z 5 14 1.54 + 0.13 2.0 + 0.2 1.84 + 0.20
(LH) (10 5 Z < 15)
15 - Z < 19 0.290 + 0.058 0.45 + 0.10 0.250 + 0.045
(MH) (16 < Z 5 19)
20 < Z < 23 0.210 + 0.051
24 5 Z 5 30 0.360 + 0.075 -0.352 + 0.018
(Fe Group)
15 < Z - 23 0.481 + 0.075 0.345 + 0.019(17 s Z 5 25)
20 < Z < 28 0.577 + 0.091 0.6 + 0.10 0.69 + 0.09
(VH)
Table 5bINTEGRAL FLUXES (particles/m2 ster sec)
Present Juliusson et al.,Charge Experiment Smith et al., 1972Group (>4.9 GV) 1973 (>5 GV) (>1.6 GeV/nuc)
10 r Z s 14 0.958 + 0.070 1.50 + 0.03 1.067 + 0.028(LH)
15 < Z 19 0.180 + 0.029 0.127 + 0.023(MH)
20 < Z < 23 0.115 + 0.026 0.112 + 0.011
24 Z < 30 0.237 + 0.044 0.30 + 0.03 0.275 + 0.014(Fe Group) 0-
15 < Z s 23 0.287 + 0.037 0.36 + 0.03 0.239 + 0.033
20 < Z 28 0.350 + 0.049 0.387 + 0.037(VH)
Table 5b (continued)INTEGRAL FLUXES (particles/m 2 ster sec)
Balasubrahmanyan Webber et al., Mewaldt et al.,
Charge & Ormes, 1973 1973 1971
Group (>4.5 GV) (>5.0 GV) (>4.9 GV)
10 . Z < 14 1.08 + 0.20(LH)
15 Z < 19 0.14 + 0.03
(NH) (16 < Z < 19)
20 Z < 23
24 < Z s 30 0.207 + 0.014-
(Fe Group)
15 Z < 23 0.30 + 0.06 0.228 + 0.014(17 < Z < 25)
20 < Z < 28 0.44 + 0.09 0.470 _ 0.034
(VH)
Table 5b (continued)INTEGRAL FLUXES (particles/m2 ster sec)
Webber & Ormes Freier & Waddington, von Rosenvinge,Charge 1967 1968 1969Group (>4.9 GV) (>4.9 GV) (>4.9 GV)
10 Z < 14 1.2 + 0.1 1.086 + 0.051(LH)
15 : Z 19 0.12 + 0.04 0.086 + 0.010 0.160 + 0.020(MAH) (16 < Z s 19)
20 < Z < 23
24 Z Z < 30(Fe Group)
15s Z 23
20 Z < 28 0.36 + 0.06 0.403 + 0.023 0.377 + 0.040(VH)
IV.B. Charge Composition, l0 Z 28
IV.B. 1. Present Experiment
The results of the charge composition study of this experi-
ment for charges ten through twenty eight are listed in Table 6. This
table lists the actual number of nuclei of each charge observed along with
correction factors as calculated in the previous chapter of this paper.
The last column shows the number of each charge, 10Z28, that would have
been observed at the top of the atmosphere by extrapolating the corrected
number of events observed back through 7.4 g/cm2 of air using the attenu-
ation mean free paths in air as directly determined in this experiment and
the latest set of fragmentation parameters in air as presented in Table 3.
The errors shown in column 4 are the cumulative effects of statistics,
errors in correction for misidentification of charges, and correction for
interactions in the detector. Errors given in column 5 reflect these
errors plus the additional error involved in extrapolating to the top of
the atmosphere, i.e. it reflects the uncertainties of about 20% in the
fragmentation parameters and about 20% in the absorption mean free paths.
The abundances at the top of the atmosphere of the charges Z = 10 - 28,
normalized to iron, are shpwn in Figure 14.
85
86
Table 6
CHARGE COMPOSITION, 10sZs28
Numbpr Correction .Number Observed Number IncidentCharge Observed Factors* (Corrected for Losses) at Top of Atmosphere
10 997 + 32 1513 + 140 1620 + 154
11 192 + 14 291 + 33 275 + 35
12 1035 + 32 (1.15 (1.32 1571 + 145 1764 + 169+0.09) +0.05)
13 164 + 13 249 + 29 254 + 31
14 776 + 28 1178 + 111 1376 + 137
15 57 + 8 78 -+ 13 69 + 14
16 249 + 16 339 + 39 350 + 42
17 47 + 7 (1.00 (1.36 64 + 11 42 + 12+0.08) +0.05)
18 137 + 12 186 + 24 165 + 27
19 42 + 6 57 + 10 26 + 15
20 158 + 13 221 + 26 229 + 30
21 34 + 6 (1.00 (1.40 48 + 9 44 + 11+0.07) +0.05)
22 113 + 10 158 + 20 117 + 28
23 66 + 8 92 + 14 61 + 22
24 103 + 10 151 + 19 117 + 31
25 46 + 7 68 + 12 70 + 22
26 412 + 20 (1.00 (1.47 606 + 54 941 + 122+0.04) +0.06)
27 14 + 4 21 + 6 33 + 10
28 24 + 5 35 + 7 54 + 19
*(Correction for events outside identification limit)(Correction for interactions in charge module)
/'
87
2.0CHARGE COMPOSITION, TOP
1.8 OF THE ATMOSPHERE
O I.6
1.4
o 1.2 r
0.8 -1 1II I
l I I0.6- l
0.4 i I
0.2 I I. / , i -
I I I' I 1 l ll I I
10 12 14 16 18 20 22 24 26 28
CHARGE
Fig= 14. Charge composition, Z = 10-28, at the top of theatmosphere, normalized to the iron abundance.
IV.B. 2. Comparison With Other Measurements
In Figures 15-16, and Table 7 the results of the relative abun-
dances of this experiment are compared to those of other workers. The
comparison between the work of various authors is sometimes difficult since
groups of elements are not always chosen in the same way. However,
recently several groups have published results on abundances of individual
charges. (Webber et al., 1972; Juliusson et al., 1972; Casse et al., 1971).
The present results are compared to these works. Also for comparison is
one set of low energy results (Cartwright et al., 1973) and one satellite
measurement (Lezniak et al., 1970, Pioneer 8) which is included since it
is free of atmospheric corrections.
Figure 15 compares the results of the present experiment to two recent
review papers, one by Tsao et al. (1973) and one by Webber (1972). These
two papers have summarized the results published to date. Both sets of
authors have weighted the summary to those results which have the greatest
statistics and best charge resolution. The greatest disagreement exists
at charges 10, 12, and 14 where the results differ by almost 15%, a seem-
ingly not large error. But since these charges are believed to be present
at the source, the discrepancies affect the predictions of the mechanism
for nucleosynthesis. (See Chapter V). A factor of two difference in the
potassium abundance is noted but due to the large statistical error in
this measurement, it is not considered serious.
Table 7 compares the results of 3 recent charge composition surveys
to the results obtained by this author (Webber et al., 1972; Casse et al.,
1971; Juliusson et al., 1972). These results were chosen for comparison
because they demonstrate charge composition as measured by several different
88
89
2.0 -* TSAO et al (1973)
_ 1.8 o0 WEBBER (1972)o O THIS EXPERIMENT
0 o
z 1.2
Z 1.0-
< 0.8
> 0.6_j-Jw 0 .4
0.2
10 12 14 16 18 20 22 24 26 28
CHARGE
Fig. 15. Charge composition, Z = 10-28, at the top of the atmos-
phere compared to the review article summaries of Webber
(1972) and Tsao et al. (1973), normalized to the iron
abundance,
Table 7
CHARGE COMPOSITION MEASURED IN THIS EXPERIMENTCOPARED TO OTHER RESULTS
Charge This Experiment Tsao et al., 1973 Webber, 1972 Webber et al., 1972 Casse et al., 1971
10 1.722 + 0.164 1.625 + 0.185 1.582 + 0.106 1.695 + 0.055 1.691 + 0.22911 0.292 + 0.037 0.249 + 0.037 0.264 + 0.035 0.276 + 0.018 0.323 + 0.10512 1.875 + 0.180 1.825 + 0.093 1.864 + 0.070 1.962 + 0.045 1.981 + 0.24813 0.270 + 0.033 0.269 + 0.093 0.264 + 0.049 0.248 + 0.018 0.543 + 0.13314 1.462 + 0.146 1.386 + 0.185 1.245 + 0.070 1.295 + 0.036 1.669 + 0.22915 0.073 + 0.015 0.050 + 0.019 0.052 + 0.014 0.043 + 0.009 0.090 + 0.04816 0.372 + 0.045 0.299 + 0.037 0.318 + 0.042 0.333 + 0.018 0.230 +.0.04017 0.045 + 0.013 0.060 + 0.019 0.063 + 0.007 0.053 + 0.009 0.060 + 0.02018 0.175 + 0.029 0.160 + 0.028 0.155 + 0.014 0.124 + 0.018 0.090 + 0.03019 0.028 + 0.016 0.070 + 0.019 0.085 + 0.021 0.114 + 0.009 0.140 + 0.030 o20 0.243 + 0.032 0.210 + 0.046 0.236 + 0.021 0.248 + 0.018 0.140 + 0.03021 0.047 + 0.012 0.030 +-0.019 0.045 + 0.007 0.038 +-0.006 0.070 + 0.02022 0.124 + 0.030 0.132 + 0.028 0.109 + 0.021 0.133 + 0.009 0.170 + 0.03023 0.065 + 0.023 0.070 + 0.028 0.059 + 0.007 0.048 + 0.009 0.050 + 0.02024 0.124 + 0.033 0.126 + 0.037 0.127 + 0.014 0.102 + 0.009 0.090 + 0.02025 0.074 + 0.023 0.070 + 0.019 0.091 + 0.021 0.081 + 0.009 0.120 + 0.03026 1.000 + 0.130 1.000 + 0.130 1.000 + 0.070 1.000 + 0.036 1.000 + 0.19027 0.035 + 0.011 0.002 + 0.004 0.037 + 0.00928 0.057 + 0.020 0.042 + 0.009 0.045 + 0.014 0.042 + 0.009
Table 7 (continued)
CHARGE COMPOSITION MEASURED IN THIS EXPERIMENTCOMPARED TO OTHER RESULTS
Charge Juliusson et al., 1972 Lezniak et al., 1971 Cartwright et al., 1973
10 1.292 + 0.033 2.665 + 0.11011 0.218 + 0.006 0.526 + 0.04812 1.700 + 0.042 2.751 + 0.11013 0.348 + 0.015 0.593 + 0.05914 1.383 + 0.033 1.986 + 0.091 1.176 + 0.11815 0.054 + 0.030 0.254 + 0.050 0.078 + 0.02016 0.269 + 0.013 0.268 + 0.060 0.196 + 0.02917 0.068 + 0.026 0.134 + 0.030 0.029 + 0.00918 0.105 + 0.028 0.196 + 0.040 0.108 + 0.02919 0.092 + 0.008 0.153 + 0.040 0.039 + 0.00920 0.213 + 0.011 0.306 + 0.060 0.127 + 0.029 -
21 0.066 + 0.018 0.077 + 0.020 0.020 + 0.00922 0.152 + 0.015 0.100 + 0.030 0.027 + 0.03923 0.089 + 0.007 0.120 + 0.030 0.039 + 0.02024 0.167 + 0.008 0.290 + 0.060 0.118 + 0.04925 0.043 + 0.025 0.200 + 0.040 0.142 + 0.07426 1.000 + 0.010 1.000 + 0.069 1.000 + 0.10827 0.017 + 0.01628 0.046 + 0.020
92
methods: Webber et al. (1972) use a combination scintillator - Cerenkov
counter detector but compensate for differences in path length using
curved detector elements; Casse et al. (1971) use as the prime measuring
element the Cerenkov detectors with spark chamber plates and photography
for trajectory determination; the Juliusson et al. (1972) experiment
makes use of gas Cerenkov counters for high energy charge composition
measurements. A comparison of the results in more detail follows.
The only discrepancy that exists between the Webber et al. (1972)
results and the results presented here occurs at charge 19. This is
certainly not a serious discrepancy. The error bar is large on potassium
due to its low absolute abundance. In addition, potassium is difficult
to separate from its much more abundant neighbor, calcium. The relative
abundance for silicon differs by about 15% between the 2 experiments.
However the error bars do overlap, bringing the values into reasonable
agreement (less than la).
The results of Casse et al. (1971) differ in many minor respects from
the results obtained here. Statistically their results are about a factor
of 3 poorer, which could explain these differences. In most cases in fact,
the large statistical error bars on their measurements bring their results
into agreement with those reported here.
Less neon relative to iron is detected by Juliusson et al. (1972) than
the present results and when compared to other authors. However, this
discrepancy is only lo in most cases. Charge 23 has a large statistical
error bar due to its low absolute abundance and also agrees to within la
of these results.
The satellite results (Pioneer 8) of Lezniak et al. (1970) and the low
93
energy (40-450 MeV/nuc.) data of Cartwright et al. (19.73) are included for
completeness. Satellite results of course are not subject to atmospheric
corrections. However, the results of Pioneer 8 do not agree very well at
all with the bulk of balloon launched experimentp. As can be seen from
Figure 16, all charges relative to iron are overabundant when compared to
atmospheric experiments. In particular chromium and manganese are over-
abundant by factors of 2 and 3 respectively relative to balloon borne
experiments, leading this author to believe that some iron has been misiden-
tified as these lower charges, thus reducing the iron abundance and increas-
ing the relative abundances. There are no serious discrepancies between
the present results and those at low energy (Cartwright et al., 1973) when
account is taken of the large statistical error in their measurements,
although there appears to be a systematic underabundance of even nuclei
relative to iron when compared to the present experiment. This results
however, from the fact that their data lumps charges 25-27 together as iron,
resulting in a larger iron abundance than is present. Another interpretation
of this data has come to light in recent measurements of the charge composi-
tion at various energies (Webber et al., 1973; Balasubrahmanyan and Ormes,
1973; Smith et al., 1973; Juliusson et al., 1972; Casse et al., 1971).
Results of these experiments indicate that the energy spectrum of iron
group nuclei is not as steep as the energy spectra of other groups of
nuclei. Therefore the ratio relative to iron of these other elements
decreases with increasing energy. The results of Lezniak et al. and
Cartwright et al. were taken at low energies where the ratio (Z=10-14)/
(Z=24-28) would be higher than in the present experiment which is taken
at high energies.
94
3.0
2.8 - 0 CARTWRIGHT et ol (1973)SLEZNIAK et al (1970)
2.6- 0 THIS EXPERIMENT
2.4
O0 2.2
n. 2 .0 "
o 1.8 -z
o 1.6zm 1.4- -
> 1.2 o
-I 1.0-
0.8
0.6
0.4--0,
0.2- 0o_ "_ o o <O
10 12 14 16 18 20 22 24 26 28CHARGE
Fig. 16. Charge composition, Z = 10-28, at the top of the atmos-phere compared to the low energy results of Cartwrightet al. (1973) and Lezniak et al. (1970), normalized toiron.
95
Mentioned in passing are two other experiments: the pioneer work in
this field by von Rosenvinge (1969) and the large exposure factor experi-
ment of Mewaldt et al. (1973). von Rosenvinge's results, although statis-
tically extremely poor, nevertheless agree within errors with the results
of the present experiment and the bulk of larger, more sophisticated experi-
ments. Mewaldt et al. have published the most significant statistical
survey to date. However, their experimental charge resolution is so poor
that they could identify only even charges with certainty. Therefore,
their results were not included for comparison.
V. INTERPRETATION OF EXPERIMENTAL RESULTS
V.A. Extrapolation Back to Source
After leaving their source region, cosmic rays diffuse through
interstellar space. During the propagation of these charged nuclei
through interstellar matter, the nuclei will be subject to the effects
of the matter and the magnetic fields traversed. The matter affects the
primary cosmic radiation through energy loss due to ionization processes
and charge alteration due to nuclear interactions. The magnetic fields
isotropize the arrival direction of the nuclei and may affect the energy
of individual nuclei through acceleration and/or deceleration. The
magnitude of the-effect of matter depends both on the nature and on the
amount of matter traversed, which in turn depends on the configuration and
strength of the magnetic fields experienced by nuclei during their traversal
of the medium.
Charge ratios outside the solar cavity depend importantly on the
characteristics of the propagation of the primary cosmic radiation in
interstellar space, and on the injection spectra which may not be identical
from charge to charge. Cosmic ray nuclei arriving at the boundary of the
solar cavity then would not be expected to have the same relative charge
abundance that they have at the source, due to the effects of the propaga-
tion. One may ask: what is the initial distribution (source distribution)
of elements which, enroute to the solar cavity, would be transformed to
the observed distribution, and how does one find this source distribution?
In the previous section, the charge distribution outside the solar
cavity is presented. The final step in the analysis is to reverse the
process outlined in the previous paragraph and "propagate" the data back
96
97
to the source. This source composition can then be examined for its
possible meaning. In this section then, by assuming various propaga-
tion parameters such as fragmentation probabilities, interaction mean
free paths, ai exponential distribution of path lengths, and the experi-
mentally observed charge composition, restrictions can be placed on the
source composition.
In any attempt to discuss the propagation of cosmic ray nuclei
through interstellar material and the consequent distortion of the charge
composition, it is first of all necessary to make some general assumptions
regarding the model of the Galaxy and the source model to be used in the
calculations. Regarding the source model: it will be assumed that the
source spectra of all multiply charged nuclei have the same shape, and
further that it is to be a power law in total energy. Another assumption
that must be made is that the light nuclei, Li-Be-B 1are absent at the
source, i.e. they are all secondary, but this assumption is of no conse-
quence here since the results are confined to 10 _ Z : 28. (These elements
are known to be absent in.the solar system abundances, a fact which can
be explained by their high nuclear reaction rates at the temperatures
obtained in the solar interior: nuclear reactions proceed quickly enough
to consume them completely. Extrapolation of this result to stellar
interiors, which have as high or higher temperatures, is therefore not
unreasonable.)
The leaky box model (Gloeckler and Jokipii, 1969) of the Galaxy will
be used in the following analysis. This model assumes the cosmic ray
sources are uniformly distributed in a spherical volume in space with the
Sun at the center, that particle emission is constant in time, and that
98
equilibrium is established between creation and loss. Cosmic rays then
diffuse through and are confined to this region which is bounded, although
there is a finite probability for escape which can be characterized by
a mean life against escape, T, commonly referred to as the leakage life-
time. This model is probably most realistic from the point of view of
the current understanding of the cosmic ray origin-propagation problem and
magnetic field structure of the Galaxy. It is mathematically equivalent
to an exponential path length distribution first suggested by Davis (1960).
The exponential path length is smooth, is strongly weighted toward short
path lengths but also contains very long path lengths, and is assumed to
be independent of the energy/nucleon of the particle.
It is assumed that particle propagation is the same for all
charges apart from the effects of interactions. It is assumed cosmic rays
are not accelerated or decelerated in interstellar space. The effects of
energy loss through ionization are also excluded. Parker shows that these
effects are negligible for particles above 4.5 GV rigidity (Parker, 1966).
Cowsik et al. (1967) showed that for steady state propagation, the effect
of ionization loss is not very drastic for heavy nuclei even at the lowest
energies of several hundred MeV/nucleon. Gloeckler and Jokipii (1969) find
ionization energy loss only significant below about 200 MeV/nucleon. The
energy losses for all nuclei under consideration here are less than 20%, as
found by Beck and Yiou (1968), e.g. at 1.5 GeV/nucleon the energy losses
along a generally accepted cosmic ray path of 5 g/cma are about 250 MeV
for an iron nucleus, which is only 15%. Error due to neglect of energy loss
processes is further minimized since only charge ratios of integral fluxes
over a limited region are treated. Further, it is assumed that at high
99
energy, (relativistic) comsic ray transport is independent of energy.
Lastly, it is assumed that the interstellar medium is composed of
pure hydrogen. This assumption is not of much consequence since the
effects of ionization energy loss have been excluded already. However
even with ionization energy loss, this assumption is still valid.
Durgaprasad considered propagation in an ionized medium of pure (-89%)
and ionized (-4%) hydrogen, and pure (-6%) and ionized (~1%) helium
(Durgaprasad, 1968). He showed there was no significant difference between
the rate of energy loss in the pure hydrogen medium and the "combination"
medium which approximated interstellar space.
With the previously mentioned assumptions, one can determine how the
cosmic ray charge distribution is altered by fragmentation as the particles
propagate from sources to the observer by solving the following system of
differential equations, which describe the collisional breakup of parent
nuclides, and the production and loss of secondary ones in successive
increments of path length:
N1 +(- - .- (22)
Here Ni(x)is the number of nuclei of the ith charge component at a distance
x g/cma from the source. The first term on the right is the loss due to
nuclear interactions which alter the identity of a nucleus, the second term
is the loss due to leakage, the third term is production of secondary
nuclei due to nuclei of greater Z. The first and second terms can be
combined together to form an effective absorption mean free path:
1 = + 1. (23)A Ai A
100
In order to solve this set of equations which extrapolates the observed
charge spectrum back to the hypothetical source region, one needs to know:
1. the nuclear interaction cross sections for each isotope
passing through interstellar space, from which are calcu-
lated the fragmentation probabilities, (.e. the probability
that a particular fragment will be produced in a nuclear
interaction), and the absorption mean free paths in hydrogen,
2. the path length distribution of nuclei during their diffusive
travel from source to detector.
Most of the nuclear parameters of 1. are not well known experimentally.
These parameters have been calculated from the semi-empirical cross
section formula of Silberberg and Tsao (1973) rather than Rudstam (1966).
They derive their formula using Rudstam's formula as a basis but using new
experimental values for cross sections not available to Rudstam. The
errors calculated from their formula are much smaller, with standard
deviations of about 10-20%, than Rudstam's formula, with factors of 2-4,
when compared to experimentally known values. The parameters have been
obtained from Silberberg and Tsao (private communication, 1973) with the
aid of their computer algorithm that gives values for energies >2.3 GeV/
nucleon, at which energy they become constant, for the most abundant
isotopes between iron and neon. (The errors involved in using the para-
meters down to 1.5 GeV/nucleon are small, s 5%). The values of the frag-
mentation parameters used are given in Table 8. Since the interactions
occur in a low density medium where the nuclei spend a long time, all
radioactive nuclei produced have been assumed to decay to stable end
products, except those whose sole mode of decay is K-capture and those with
half-lives greater than 106 years. The fragmentation probabilities,-given
Table 8
FRAGMENTATION PROBABILITIES FOR COLLISIONSWITH HYDROGEN (Silberberg and Tsao, 1973)
Target 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
Product
26
25 .0490
24 .1212 .1179
23 .0712 .0766 .0787
22 .0955 .1026 .1197 .1361
21 .0182 .0184 .0236 .0243 .0270
20 .0545 .0567 .0661 .0762 .0894 .1084
19 .0303 .0322 .0362 .0421 .0506 .0612 .0628
18 .0500 .0521 .0567 .0697 .0809 .C962 .0646 .0914
17 .0212 .0245 .0268 .0324 .03F6 .043' .0305 .0438 .0537
16 .0424 .0444 .0488 .0551 .0675 .0804 .0503 .0705 .0875 .1112
15 .0136 .0153 .0142 .0178 .0219 .0227 .0144 .0210 .0239 .0288 .0280
14 .0318 .0337 .0378 .0438 .0523 .0612 .0359 .0514 .0616 .0741 .0862 .1287
13 .0136 .0138 .0142 .0178 .0202 .0227 .0108 .0171 .0199 .0226 .0216 .0345 .0411
12 .0273 .0291 .0315 .0357 .0422 .0490 .0287 .0438 .0457 .0535 .0625 .0897 .1111 .1476
11 .0106 .0123 .0126 .0146 .0169 .0192 .0090 .0133 .0159 .0185 .0172 .0253 .0290 .0356 .0485
10 .0212 .0230 .0252 .0376 .0337 .0385 .0233 .0305 .0358 .0391 .0453 .0598 .0725 .0891 .1078 .1552
102
in Table 8, are calculated from
Pji = P(Zt, At; Zp, Ap) (24)
Ap t t p t
where a (Zt, At; Zp, A p) is the nuclear interaction cross section for
the production of element (Zp, AP) from-element (Zt, At) and at is the
total inelastic cross section of element (Zt, At) with
at = 10 (1.25)2 [A2/3 - 1] (25)
(Silberberg and Tsao, private communication, 1973). The absorption mean
free paths in hydrogen, given in Table 9, have been calculated from Ai =
mp/ai where mp - mass of the proton.
The problem of what form of distribution of path lengths goes to make
up the average amount of interstellar matter traversed is not well under-
stood, and deserves a few more remarks than given in the introductory para-
graps of this section. Models used have ranged from a distribution that
is a 6-function (simple slab approximation) in which all particles traverse
the same amount of matter, to a Gaussian distribution centered on some mean
value, which arises from considering a point source in a homogeneous iso-
tropic diffusive medium (Balasubrahmanyan et al., 1965), to an exponential
distribution @(x) dx = a e-ax which arises from considering propagation in
a bounded medium (Cowsik et al., 1967). The slab model is used for atmos-
pheric corrections but is physically artificial for interstellar propaga-
tion. The Gaussian distribution, although physically more realistic, does
not fit experimental evidence and can also be rejected. (Shapiro et al.,
103
Table 9
ABSORPTION MEAN FREE PATHS IN HYDROGEN
Charge MFP(g/cm)
10 5.14
11 4.80
12 4.50
13 -4.25
14 4.03
15 3.84
16 3.60
17 3.44
18 3.32
19 3.18
20 3.00
21 2.92
22 2.82
23 2.71
24 2.63
25 2.56
26 2.53
104
1970b) Calculations done by several authors indicate that not only is
the exponential distribution the most physically realistic , but it fits
the existing data most accurately. Shapiro et al. (1970a, b) found the
slab model could not reproduce the observed abundance of L-nuclei given
the observed abundance of 17 Z 25 which are produced'from iron nuclei.
They found the exponential vacuum path length with exp (-016 + 0.04) x
fit the observed charge ratios at high energies (E > 1.5 GeV/nucleon) best.
Cowsik et al. (1967) conclude that the generally used matter-slab approxi-
mation for interstellar matter traversed by cosmic radiation leads to an
erroneous interpretation of the experimental data. They find that the
matter slab is inconsistent with low energy data and show that propaga-
tion of cosmic rays must involve a wide distribution of path lengths
(Cowsik et al., 1970). The data collected by von Rosenvinge and his
analysis (von Rosenvinge, 1969) is also consistent with an exponential
path length. Mewaldt et al. (1971) also conclude that the simple slab
model does not fit their data but an exponential does. Using new measure-
ments for production cross sections, Shapiro et al. (1971) still find the
observed L/M ratio and (17 s Z 25)/Fe ratio can be reproduced best by a
pure exponential distribution of path lengths of the form exp (-0.23 x) for
x > 1 and a linear increase from zero to 1 g/cm2
The treatment here then will be limited to the pure exponential vacuum
path length distribution of the form:
daN exp (-x/xo) (26)
IThe exponential path length distribution arises from a uniform sphericaldistribution of sources in a bounded medium with the Sun at the center.Fichtel and Reames (1966), however, have deduced strictly from diffusiontheory an exponential-like distribution so similar to a pure exponentialthat its application to existing data can not differentiate between them.
105
where x is the mean path length traversed by cosmic rays, or age since
Xo = OcnmpT where T is cosmic ray age; The exponential distribution used
here is dN/dx = e-o'0 . x as shown in Figure 17.
Using the values given for the propagation parameters and an exponen-
tial path length distribution in the differential equations indicated
previously, it is relatively easy to calculate from the observed charge
spectrum what the equivalent spectrum should have been before passage
through some assumed mean amount of matter. One starts with the.heaviest
element, iron, and assumes there is no fragmentation into the iron group
from heavier nuclei (the ratio [Z 30]/Fe is < 10-s). The calculations
have been performed according to the matrix solution method outlined in
von Rosenvinge (1969). The method calculates the source abundance of each
element in turn beginning with iron nuclei by extrapolating the abundance
of each element back through an exponential path length distribution of
matter, before calculating the source abundance of the next lower element.
This allows the abundance of any one element to increase or decrease as
secondaries, tertiaries, quaternaries, etc. enter its abundance and secon-
daries, tertiaries, quaternaries, etc. leave the abundance. This procedure
can result in negative abundances of certain elements before the extra-
polation is complete. Each charge is considered to have contributed to
fragmentation only so long as the abundance of that element is positive.
When the abundance of an element reaches zero or goes negative, that abun-
dance is "frozen" at zero in the calculation so that it can not contribute
further to secondary production during the calculations of succeeding lower
elements. This fragmentation would produce "negative" secondaries which
would incorrectly decrease the abundance of lower elements. Clearly a
DISTRIBUTION OF COSMIC RAYPATH LENGTHS
1.0
dN/dx X e- o xI-
z
a 0.5-
Z
5 10 15
x( g/cm2 )
Fig. 17. Exponential distribution of cosmic ray path lengths, dN/dx e-0 ' oX
107
limit is set on such an extrapolation if many of the deduced abundances
become negative. If these negative abundances reach significant values,
this implies it is physically unreasonable to postulate propagation through
as much matter as assumed. This sets an upper limit on the amount of
matter traversed. (However it is not possible to set a lower limit from
heavy nuclei alone since the primary spectrum has a variable path length
distribution. To establish a lower limit, an independent piece of infor-
mation, such as the L/M ratio, must be used). Slight negative abundances
of a few individual elements also may be used to test the assumption that
these nuclei are absent in the sources.
The detailed predictions of these calculated extrapolations lead to
the source composition shown in Figure 18. Numbers for the source abun-
dances relative to iron and the error bars are given in column 3 of Table
11 where they are also compared to solar system abundances. Errors on
the relative abundances are due to the effects of errors in the composition
at the top of the atmosphere and uncertainties of about 20% in the fragmen-
tation probabilities and absorption mean free paths. Errors due to compo-
sition uncertainty range from less than 1% at sodium to 60% at chlorine
and vanadium. Errors due to uncertainty of the fragmentation parameters
range from 1% at silicon to about 60% at chlorine, titanium, and vanadium.
Errors due to uncertainties in the mean free paths range from less than 1%
at silicon to about 60% at chlorine, titanium, and vanadium. Generally,
for a given element, the fragmentation probability contributed the largest
portion of the cumulative error, it being a factor of 2 larger than other
errors. In all cases, errors in the absorption mean free paths were the
smallest contributors to the cumulative error.
Various forms of an exponential distribution of path lengths were tried.
108
2.0 - 0 CHARGE COMPOSITIONTOP OF ATMOSPHERE
1.8 * COSMIC RAY SOURCEo COMPOSITION
UI.4
z I.2
z2 1.0-
<0.8w> 0.6
w 0.4
0. 2* *
I II I 9 I
10 12 14 16 18 20 22 24 26 28
CHARGE
Fig. 18. Comparison of cosmic ray source composition to thecosmic ray charge composition at the top of theatmosphereo
109
Limits on the distribution were established as exp(-0.16x) to exp(-0.24x)
which correspond to mean amounts of matter of 6.3 g/cm2 and 4.2 g/cm?
respectively. The lower limit is established at the thickness of matter
where the first element reaches zero or goes negative. This occurred fo:
potassium after about 4.2 g/cm2 . After this amount of matter however, most
other secondary elements such as chlorine, scandium, and vanadium still
had positive abundances. The upper limit is established by requiring
the abundances of all charges 21-25 to reach zero or go negative. Of
course, after this amount of matter, elements such as chlorine, argon,
and potassium had large negative abundances. After a mean amount of matter
of 5.0 g/cm2 , the abundances of argon and potassium were only slightly
negative, chlorine and vanadium were zero, and scandium, titaniun, chromium,
and manganese were only slightly positive. This was chosen as the optimum
value: 51'1.3 g/cm2 for the mean amount of matter cosmic rays have traversed.
From Figure 18 it can be seen that by x = 5 g/cm2 the average abun-
dance of the elements 15 and 17 to 19 is zero. The abundances of nuclei
21 ! Z 25 are also nearly zero at about 5 g/cm2 . These nuclei are thought
to be due to the interstellar fragmentation of iron since their abundances
are very low in the solar system, only about 0.02 that of iron (Cameron,
1973). Hence one must conclude that heavy nuclei in cosmic radiation cannot
have traversed much more than 5 g/cm of interstellar matter, although they
could have traversed less, if one assumes these nuclei are present at the
,source.
There appear to be finite abundances of S and Ca at the source. The
source ratios of these elements are: Ca/Fe = 0.18 +0.01, S/Fe = 0.29 +0.02.
The data is therefore consistent with a source consisting predominantly of
110
iron, silicon, magnesium, and neon with small percentage admixtures of
S and Ca. The mean matter length x = 5 g/cm 2 resulting from an expo-
nential path length distribution is also consistent with values found to
fit the L/M ratio and VVH nuclei. (Gloecklcr and Jokipii, 1969, find a
value of 4.0 +0.8 g/cm2 using the L/M ratio; Cowsik et al., 1970, find
a value of 5.3 to 8.6 g.cm using VVH data; Shapiro et al., 1970, find avalue of 6.26 +2.08
value of 6.26 -1.25 using the L/M ratio and letting the abundance of
Z = 17-25 go to zero; Fowler et al., 1970, find a value of 4.0 +2.0
g/cm2 using their VVH data).
V.B. Cosmic Ray Age - Amount of Matter in Interstellar Space
Nuclei in the charge range Z = 17-25, in particular odd charges
17 and 19, and all charges 21-25, are believed to be produced mostly by
spallation reactions of iron and its passage thorugh interstellar matter
(Lezniak et al., 1970). This implies their source composition is zero.
If one assumes that the mean amount of matter traversed is that which
is found by extrapolating the observed composition back through sufficient
material such that these abundances become zero, as done in the previous
section, then this estimate of the mean amount of matter through which
cosmic rays have passed leads to an estimate of the age of cosmic rays.
The mean density of matter in interstellar space traversed by cosmic ray
nuclei is related to x, the total amount of matter traversed in g/cm by
the relation
- (27)x = p Bc T
Here Oc is the mean velocity of nuclei. For this experiment B - 1 (rela-
tivistic cosmic rays). The quantity x as determined in the previous
section is 5.0 g/cm2 . With the generally accepted assumption of the
average density of interstellar space in the disc of one hydrogen atom per
cubic centimeter (if cosmic rays are confined to the disc), this leads to
time 7 - 3.2 !08 x 108 years which cosmic rays must spend in the disc.
Another method exists for the determination of the age of cosmic rays:
using as the measuring device the time dilated decay of Be- . moving with
relativistic velocity. This isotope has a half-life at rest of 1.5 x 10s
years and is suitable for the measurement of ages in the range 106 - 108
years. This method consists of measuring the isotopic abundance of beryllium
or the variation with energy of the ratio of beryllium to boron. The age
is then estimated from the ratio
111
112
BelO/Be7+9+10
which depends on the amount of time Belo has had to decay; or the age ,is
estimated from the ratio
Be/B
which should vary with energy due to the.time dilation of the decay of
Belo to Blo via the reaction
Belo 4 B10 + e + v.
These two ratios measure cosmic ray age directly. They give T - 3.4 x 106
years (Webber et al., 1973) a value which is in good agreement with the value
obtained here (nb: the estimate of cosmic ray age using beryllium and boron
abundances depends on x, the mean amount of matter through which cosmic
rays have passed, but is independent of p, the average ihterstellar density.
However the mean amount of matter can be estimated by other means such
as the L/M ratio, and does not depend on the value found here for heavy
particles. Hence these 2 estimates of cosmic ray age can be considered
to be independent of each other).
V.C. Comparison to Solar System Abundances
Before comparing the cosmic ray source composition to solar system
abundances, the cosmic ray source composition obtained in this paper will
be compared to results obtained by other authors. Several authors have
recently published possible source abundances of cosmic ray nuclei in the
charge range 10Z:30, including von Rosenvinge (1969), Shapiro and
Silberberg (1970b), Ramaty and Lingenfelter (1971), Shapiro et al. (1971),
Cartwright et al. (1971), Webber et al. (1972), and Shapiro et al. (1973),
using a variety of forms of an exponential distribution of path lengths
and fragmentation parameters from Rudstam's equations and from Silberberg
and Tsao's equations. Table 10 li4ts the cosmic ray source composition
deduced by several authors (Webber et al., 1972; Ramaty and Lingenfelter,
1971; Shapiro et al., 1973) including the results calculated here.
This paper uses an exponential distribution exp(-0.20x) with the Silberberg
and Tsao parameters, Shapiro et al. (1973) use an exponential distribution
exp(-0.24x) for x > 1 g/cm2 and a linear rise from x = 0 to x = 1 g/cm2
with the Silberberg and Tsao parameters, Ramaty and Lingenfelter (1971) use
an exponential distribution exp(-0.20x) with the Rudstam parameters, and
Webber et al. (1972) use an exponential distribution exp(-0.20x) with an
earlier form of the Silberberg and Tsao parameters (Shapiro and Silberberg,
1970a).
Upon comparison of this work to these authors, one concludes that there
are still wide variations in the deduced cosmic ray source composition.
The wide variations are not completely explained as due to the different
exponential forms for path length distribution and Rudstam's parameters or
Silberberg and Tsao's parameters used by the various authors. Factors of
113
Table 10
COMPARISON OF DEDUCED COSMIC RAY SOURCECOMPOSITION OF SEVERAL AUTHORS
This Shapiro Ramaty and WebberCharge Calculation et al. (1973) Lingenfelter (1971) et al. (1972)
10 1.443 + 0.121 0.780 + 0.098 0.850 0.868 + 0.02911 0.185 + 0.024 0.039 + 0.020 0.040 0.067 + 0.02012 1.684 + 0.077 1.122 + 0.098 1.110 1.200 + 0.03513 0.205 + 0.015 0.098 + 0.049 0.051 0.110 + 0.02214 1.375 + 0.052 0.995 + 0.146 0.890 0.890 + 0.03015 0.042 + 0.007 0.010 + 0.010 0.002 0.010 + 0.01016 0.294 + 0.021 0.146 + 0.029 0.130 0.175 + 0.02517 0.005 + 0.005 0.0 0.0 0.010 + 0.01018 0.0 + 0.010 0.034 + 0.024 0.032 0.015 + 0.01519 0.0 + 0.010 0.0 0.0 0.019 + 0.01220 0.180 + 0.010 0.107 + 0.039 0.0 0.130 + 0.02021 0.027 + 0.007 0.0 0.0 0.015 + 0.01522 0.035 + 0.035 0.0 0.0 0.035 + 0.02223 0.005 + 0.005 0.0 0.0 0.010 + 0.01024 0.036 + 0.024 0.015 + 0.015 0.20 0.030 + 0.03025 0.047 + 0.015 0.010 + 0.010 0.045 0.025 + 0.01526 1.000 + 0.130 1.000 + 0.146 1.000 1.000 + 0.03327 0.035 + 0.007 0.0 0.028 0.057 + 0.007 0.039 + 0.010 0.035 + 0.007
115
4 and 5 differences occur between the Rudstam, and Silberberg and Tsao
parameters which could explain the variations between the Webber et al.
results, the Ramaty and Lingenfelter results, and those reported here.
A 20% error iL the fragmentation parameters accounts for about 1/2 of the
errors on the deduced source abundances quoted here. This would not
explain the variation between the Shapiro et al. results and those reported
here since the same fragmentation parameters were used. It is not believed
that the variation in source composition is due to the exponential distri-
bution of path length chosen: Ramaty and Lingenfelter (1971), using
several propagation models, conclude that the source abundances are not
strongly model-dependent, a conclusion also reached by this author. Rather
it is suggested that the wide disparity between the deduced source compo-
sition of various authors is due to compositional uncertainties at the top
of the atmosphere. Errors in the composition at the top of the atmosphere
account for the remaining 1/2 of the error in the deduced source abundance
of most elements quoted here. In the last few years, subtle but signifi-
cant changes have occurred in the cosmic ray composition at the top of the
atmosphere, for example the chromium abundance mentioned in the next para-
graph. These changes are probably responsible for the variations in the
deduced cosmic ray source composition since the results reported here begin
with the Ramaty and Lingenfelter work in 1971 up through to the present work
in 1973.
The results of this investigation reveal that the elements neon, mag-
nesium, silicon, and iron dominate the distribution. Sulfur must also be
present at the source in large amounts relative to iron. Calcium is
definitely present in cosmic ray sources but there is probably no source
116
abundance of argon in agreement with Shapiro et al. (1973) and Webber
et al. (1972). Earlier experimental measurements showed a sizable Cr/Fe
ratio at both high and low energies (Mathieson et al., 1968; Waddington
et al., 1970; Lezniak et al., 1970; Dayton et al., 1970; Price et al.,
1970; Garcia-Munoz and Simpson, 1970), forcing the conclusion that sub-
stantial chromium existed at the source (Shapiro and Silberberg, 1970b;
von Rosenvinge, 1969; Ramaty and Lingenfelter, 1971). More recent measure-
ments with better resolution and greater statistics show a lower flux of
chromium (Binns et al., 1971; Webber et al., 1971; Casse et al., 1971;
Mewaldt et al., 1973). The chromium abundance observed in this experiment
is low enough to conclude that it is principally secondary in origin, in
agreement with the conclusions of Shapiro et al. (1973) and Webber et al.
(1972).
If one somewhat arbitrarily states that a source abundance is "real"
if less than 25% of the abundance at the top of the atmosphere were due to
secondaries, then one can conclude that the trend of the most recent experi-
mental and theoretical work favors finite source abundances in this charge
range of neon, magnesium, silicon, sulfur, calcium, and iron. If > 50% of
the abundance of an element observed at the top of the atmosphere is due to
spallation, then these elements probably do not exist in the sources.
Elements in this group are Cr, V, Ti, Sc, K, Ar, Cl, and P. The region from
25-50% secondary production is nebulous and probably indicates some source
abundance. The source abundances are probably r 0.20 of iron, with large
uncertainties attached. Elements in this group are Mn, Al, and Na.
After extrapolation back to the cosmic ray source region, the cosmic
ray source abundances (CRS), although similar in general features, are
different from the solar system abundances ihen examined for fine points of
117
detail. Table 11 and Figure 19 compare the deduced cosmic ray source
composition to the solar system composition as reported by Cameron
(Cameron, 1973), both relative abundances normalized to iron, Z = 26. The
abundances given by Cameron in this paper are intended to represent the
typical values in the solar system, or for normal main sequence stars.
These solar system abundances (SS) are derived from meteorites, solar
photosphere and chromosphere spectroscopic measurements, with some input
from measurements of energetic solar particle abundances, and a few inter-
polated values values based on nucleosynthesis theory. The following
discussion examines in more detail the finer points of the table and
figure where the CRS and SS abundances differ.
In general, there is a relative richness of heavy nuclei in the cosmic
rays with a strongly peaked iron group and a large even-odd effect, when
compared to the SS abundance. Neon, magnesium, silicon, and sulfur are
clearly present in cosmic rays. The presence of these elements in
cosmic rays, however, indicates a somewhat different evolution than the
solar system. Although neon is underabundant in CRS relative to SS, the
value for neon in the SS comes from solar cosmic ray observations which
come from solar flare events, and hence may not be representative of the
"universal" SS abundance. The ratios CRS/SS for magnesium and silicon
are very close to 1. There is a large uncertainty in the SS abundance of
sulfur. Cameron chose 0.6 because this amount can be produced by nucleo-
synthesis under hydrostatic equilibrium conditions which is the process
believed to be responsible for the elemental abundances in the sun.
The odd elements, sodium and aluminum, have ratios CRS/SS which are
still close to 1 suggesting they might have a common origin.
118
Table 11
COMPARISON OF' SOLAR SYSTEM ABUNDANCESTO COSMIC RAY SOURCE ABUNDANCES (NORMALIZED TO IRON)
Charge SS (Cameron, 1973) CRS CR (Top of Atmosphere)
10-Ne 4.14 1.443 + 0.121 1.722 + 0.164
11-Na 0.072 0.185 + 0.024 0.292 + 0.037
12-Mg 1.278 1.684 + 0.077 1.875 + 0.180
13-Al 0.102 0.205 + 0.015 0.270 + 0.033
14-Si 1.205 1.375 + 0.052 1.462 + 0.146
15-P 0.012 0.042 + 0.007 0.073 + 0.015
16-S 0.602 0.294 + 0.021 0.372 + 0.045
17-Cl1 6.867x10-3 0.005 + 0.005 0.045 + 0.013
18-Ar 0.141 0.0 + 0.010 0.175 + 0.029
19-K 5.060x -3 0.0 + 0.010 0.028 + 0.016
20-Ca 0.087 0.180 + 0.010 0.243 + 0.032
21-Sc 4.217x10- 0.027 + 0.007 0.047 + 0.012
22-Ti 3.343x10 -3 0.035 + 0.035 0.124 + 0.030
23-V 3.157x10-4 0.005 + 0.005 0.065 + 0.023
24-Cr 0.015 0.036 + 0.024 0.124 + 0.033
25-Mn 0.011 0.047 + 0.015 0.074 + 0.023
26-Fe 1.000 1.000 + 0.130 1.000 + 0.130
27-Co 2.663x10-3 0.034 + 0.005 0.035 + 0.011
28-Ni 0.058 0.060 + 0.007 0.057 + 0.020
119
1645 157
0
II
0
- 10I
C,
I0 12 14 16 18 20 22 24 26 28 30
Fig. 19 Comparison of cosmic ray source composition to solar
z
0.0 ±1.91
0.0±.07
10 12 14 16 18 20 22 24 26 28 30CHARGE
Fig. 19. Comparison of cosmic ray source composition to solarsystem abundances, normalized to iron.
120
Examination of Table 11 reveals the relative rarity in the SS of
elements of chlorine to manganese, which is also true of CR source abun-
dances. The argon abundance is an anomaly: there is no argon in cosmic
ray source regions. This is a significant disagreement with the SS where
some argon appears to exist. However, it should be noted that the SS argon
value is poorly known. Cameron's abundance value for A36 is simply an
interpolation between the observed abundances of S32 and Ca4o
Table 11 and Figure 19 indicate a cosmic ray excess at calcium, and
the heavier elements around the iron peak, chromiumand manganese. Only
about one quarter of the calcium has resulted from fragmentation, implying
that this element had to be present at the source. In the Z = 21-25 region,
the overabundance of chromium and manganese in the CRS relative to SS
abundances is apparent, along with possible overabundances of titanium and
vanadium.
Although cobalt and nickel were not extrapolated back to the source
region, the source abundance should be about the same as that detected at
the top of the atmosphere since the spallation contribution to these two
elements from elements Z 30 is negligible and loss processes should be
identical to iron.
The differences in the CRS and SS abundances examined in the preceding
discussion are not as regular as might be expected if cosmic rays were
preferentially accelerated from a sample of solar-like material. If the
CRS/SS ratios are the same (equal to 1) then cosmic rays must have been
formed by the same mechanism that produces elements in the Sun, but if the
ratios are not equal, the abundances may be compared to other models in an
attempt to determine the formation process for their origin. Knowledge
121
of the relative abundances of cosmic rays when compared to solar system
abundances places boundary conditions on models for cosmic ray production.
The differences in the relative abundances of CRS and SS suggest some
form of systematic nuclear evolution of the cosmic ray abundances beyond
that observed in solar matter.
V.D. Possible Source of Primary Cosmic Radiation
The endpoint of the study undertaken here should be to relate
the results obtained in this study on the cosmic ray source composi-
tion to the abundance distribution that might be expected to exist in
cosmic ray sources based on the predictions of nucleosynthesis theories.
In this manner, one can identify, or at least place restrictions Do, the
cosmic ray source and/or mechanisms responsible for the production of
primary cosmic radiation. For example, if cosmic radiation has its origin
in the late stages of supernova evolution, then the relative abundances
should reflect the abundances of energetic supernova ejecta.
The idea that the bulk of primary radiation is ejected during super-
nova explosions is not new (Burbidge et al.,.1957; Ginsburg and
Syrovatskii, 1964). Theoretical models of supernovae predict such vio-
lent explosions as to imply significant element synthesis up through iron
by the thermonuclear reactions that occur under these extreme conditions.
The explosion itself ejects material from the outer regions of the star,
this same material which has been processed to the iron peak by explosive
burning. If this highly energetic ejected material becomes primary cosmic
radiation, then cosmic rays should reflect the source composition of
explosive nucleosynthesis, after the effects of interstellar propagation
are removed, as stated by Arnett (1973):
"With improving data, better known fragmentation cross
sections, and a better understanding of the process of
cosmic ray propagation, the cosmic radiation may be a
powerful tool for exploring explosive events."
This author feels these conditions are now reasonably well satisfied, and
122
123
wishes to undertake just such a study as further suggested by Arnett in
that same review article.
"A detailed quantitative comparison of cosmic ray
source abundances with predictions of explosive
nucleosynthesis may soon be possible."
Up to this time, most of the predictions of the theory of explosive
nucleosynthesis have been compared to solar system abundances (cf. Arnett,
1969; Truran and Arnett, 1970; Michaud and Fowler, 1972; Arnett and Clayton,
1970; Arnett et al., 1971). The features of solar system abundance distri-
bution of elements can be reproduced with a good degree of success by
calculating the nucleosynthesis that takes place when massive stars burn
their evolved cores and outer layers violently and quickly on a hydro-
dynamic timescale. This excellent agreement suggests that supernovae can
produce the heavy element abundances through explosive nucleosynthesis.
However, the results of the predictions agree mostly with the solar system
abundances, but as pointed out in section V.C. cosmic ray composition
differs in some important respects from solar system abundances. Only
three very brief studies have attempted to compare cosmic ray relative
abundances to solar system relative abundances: Kozlovsky and Ramaty (1973)
who compared only Mg, Si and Fe; Arnett and Schramm (1973) who compared Ne,
Mg, Si, and Fe; and Mewaldt (1971) who compared only the even elements in
the charge range 16;Z-26.
An attempt will not be made here to go into the intricacies of explo-
sive nucleosynthesis. It is a topic unto itself. Only the results of the
predictions of the theory of explosive nucleosynthesis through carbon
burning, oxygen burning, and silicon burning will be presented and compared
to cosmic ray source abundances. The reader is referred to the detailed
124
papers of combinations of authors such as Arnett, Clayton, Truran,
and Woosley (cf papers referenced in the previous paragraph: Arnett (1969)
and Arnett et al. (1971) for explosive carbon burning; Truran and Arnett
(1970) for explosive oxygen burning; Clayton and Peters (1970) and Michaud
and Fowler (1972) for explosive silicon burning.)
Briefly, however, the elements neon to aluminum can only be produced
by carbon burning, silicon to calcium by oxygen burning, and the higher
Z elements by silicon burning. These various forms of explosive nucleo-
synthesis can occur in several different mass zones of a star where
boundary conditions of density and temperature are satisfied for each
form of nucleosynthesis. None of these forms of nucleosynthesis can pro-
duce the relative abundances of all the elements from charge 10 to 28 due
to "freeze-out" of nuclear reactions as expansion occurs after the explo-
sion. But if it can be assumed that conditions in different mass zones
are satisfied for each form of explosive nucleosynthesis as the explosion
proceeds outward through the star, then the results of each form of nucleo-
synthesis can be added: high Z elements would be formed in inner
zones, intermediate Z elements in intermediate mass zones, and low Z elements
in outer mass zones.
The abundances in column 5 of Table 12 represent the integrated matter
ejected from explosive nucleosynthesis of the supernova model, i.e. it
represents an integration over the products of explosive carbon burning,
explosive oxygen burning, and explosive silicon burning (cf previously
referenced papers in this section).
Can the abundances of elements in groups one and three, designated
previously as those which are known with reasonable certainty to be primary,
be produced by explosive nucleosynthesis as would occur in supernovae?
Table 12
COMPARISON OF DEDUCED COSMIC RAY SOURCE COMPOSITIONTO EXPLOSIVE NUCLEOSYNTHESIS PREDICTIONS
Composition Secondary Explosive Nucleo-Charge (Top of Atmosphere) Production Cosmic Ray Source synthesis Predictions*
Ni 0.057 0.0 0.057 + b.007 0.066Co 0.035 0.0 0.035 + 0.005 0.001Fe 1.000 0.0 1.000 + 0.130 1.000Mn 0.074 0.027 0.047 + 0.015 0.005Cr 0.124 0.088 0.036.+ 0.024 0.015V 0.065 0.060 0.005 + 0.005 0.001Ti 0.124 0.090 0.035 + 0.035 0.004Sc 0.047 0.020 0.027 + 0.007 0.0Ca 0.243 0.063 0.180 + 0.010 0.173K 0.028 0.028 0.0 + 0.010 0.003Ar 0.175 0.175 0.0 + 0.010 0.126Cl 0.045 0.040 0.005 + 0.005 0.002S 0.372 0.078 0.294 + 0.021 0.663P 0.073 0.031 0.042 + 0.007 0.001Si 1.462 0.087 1.375 + 0.052 1.389Al 0.270 0.065 0.205 + 0.015 0.109
Mg 1.875 0.191 1.684 + 0.077 1.037Na 0.292 0.107 0.185 + 0.024 0.080Ne 1.722 0.279 1.443.+ 0.121 2.565
4Taken from Arnett and Clayton (1970), Michaud & Fowler (1972), Arnett (1969), and Truran and
Arnett (1970).
126
Figure 20 compares the predictions of explosive nuclesynthesis for the
abundances of elements to the cosmic ray source composition found here
for those elements in groups 1 and 3 - Ne, Na, Mg, Al, Si, S, Ca, Mn,
Fe, and Ni. This integrated model leads tc abundance predictions which
are in good agreement within a factor of 2 or 3 with the cosmic ray source
distribution found here. Magnesium and silicon are believed to be products
of explosive nucleosynthesis. If these elements in CRS abundances have
explosive nucleosynthesis as their common origin, then the ratio (CRS/EN)
should be close to 1. The ratio close to 1 calculated here is consistent
with this viewpoint. Since argon is believed to be the product of nucleo-
synthesis of silicon with subsequent a-particle capture, its low value at the
cosmic ray source may be an important clue to the nature of nucleosynthesis
at the source, i.e. whether it is hydrostatic burning as in main sequence
stars or explosive nucleosynthesis, as in supernovae. However, the abun-
dance value of argon is not known well enough to include it for compprison
at this time. The previously noted overabundances of cosmic ray sources
relative to the solar system of Cr and Mn, and possible Ti and V, is a clue
which reveals that nucleosynthesis must have proceeded further in cosmic
ray sources than in the solar system. The ratio (CRS/EN) of Mn substanti-
ates this conclusion. (The source abundances of Cr, Ti, and V are also not
known well enough to include for comparison to models of explosive nucleo-
synthesis). However this ratio is large enough to suggest that the abun-
dance of manganese, or extrapolation of manganese back to the source is in
error. The presence of nickel in cosmic ray sources with an abundance of
5% of iron indicates that nucleosynthesis processes which terminate at iron
must not completely dominate the production of cosmic rays at the sources.
127
OO0
6) -
I Il
0
0 0 -- 4
to iron.
I--
10 12 14 16 18 20 22 24 26 28 30CHARGE
Fig. 20. Comparison of deduced cosmic ray source composition tothe predictions of explosive nucleosynthesis, normalizedto iron°
128
In fact, the presence of this level of nickel begins to open up the
possibility of choosing between alternate source nucleosynthesis models,
such as "extensive" and "complete" silicon burning predictions of Arnett
and Clayton (1970).
This author finds that the cosmic ray source abundances from neon to
iron calculated in this paper are consistent with the predictions of
different forms of explosive nucleosynthesis as would occur in different
mass zones during the supernova explosion of an ordinary highly evolved
massive star, 8 - M/M ! 70. It is suggested that these stars may be the
source of primary cosmic radiation. It should be pointed out however that
there are factors of 2 and 3 involved in the.predictions of the theory of
explosive nucleosynthesis due to uncertainties in the theory. For example,
it is not yet clear to physicists studying nucleosynthesis whether the
supernova model can produce all the elements 109Z928 in their proper
relative abundances in a single event. Can the highly evolved core of a
massive star implode, releasing an outgoing pressure wave which will trigger
explosive nucleosynthesis of overlying non-central mass zones? If the
relative abundances can not be reproduced in a single event, can the rela-
tive abundances still be produced by integrating over many events of
different types of supernovae? Can the explosion itself, or a remnant of
the explosion such as a pulsar or rotating neutron star, accelerate the
material to the high energies observed in cosmic rays? Lastly several
important isotopes known to be present in the solar system are not produced
by explosive nucleosynthesis, and must be produced under other circumstances.
Cosmic ray isotope measurements are awaited to clarify this discrepancy.
VI. Summary/Conclusions
It is appropriate at this point to summarize the results of this
paper. About 5000 events of relativistic cosmic ray nuclei with
10 ! Z r 28 with energies greater than 1.16 Gev/nuc have been observed by
the High Energy Cosmic Ray Experiment, an ionization spectrometer type
detector. These data have been analyzed for their possible meaning.
Absolute fluxes of various charge groups at various rigidities, which
have also been extrapolated to the top of the atmosphere using atmospheric
growth curves measured on ascent and descent portions of the flight, have
been presented. Integral flux values of 10 Z14 = 9.58 + 0.70 x 10-1,
15sZ:l9 = 1.80 + 0.29 x 10 -1, 20sZ23 = 1.15.+ 0.26 x 10-1, and 24 Z 28 =
2.37 + 0.44 x 10-1 particles/m -sec-ster for rigidity geater than 4.9 GV
and 105Z14 = 1.54 + 0.13 x 100, 15fZ 19 = 2.90 + 0.58 x 10-1 and 24iZi28 =
3.60 + 0.75 x 10- particles/m 2-sec-ster for rigidity greater than 3.25 GV
are reported. These results are compared to other recent measurements at
similar geomagnetic latitude. The fluxes measured are generally consist-
ent but systematically seem to be lower than those measured by other
workers
Measurements of the relative abundances of these elements are in general
agreement with previous results although the results presented here differ
in fine detail. It is felt that the results reported in this paper repre-
sent an advancement over previous results due to the combination of the
large statistical nature of the survey and good charge resolution. The
results at the top of the atmosphere reported here for the more abundant
elements relative to iron are: Ne/Fe = 1.722 + 0.164, Mg/Fe = 1.875 + 0.180,
Si/Fe = 1.462 + 0.146, Ca/Fe = 0.243 + 0.032. Agreement amongst various
129
130
workers (Cartwright et al., 1973; Webber et al., 197.2; Casse et al.,
1971; Juliusson et al., 1972) in the field of cosmic radiation is now
within Iq for these more abundant elements. Agreement for the less abun-
dant elements is not as good, probably as a result of poor collection
statistics and difficulties is separating these elements from their more
abundant neighbors. For example, results reported here for potassium and
vanadium are: K/Fe =0.028+ 0.016 and V/Fe = 0.065 + 0.023. These results
differ from those of other workers mentioned above by factors of 2 and 3
in some cases, although error bars are so large that the measurements can
be said to agree due to overlap of data. This charge composition observed
at balloon depth has been extrapolated to the top of the atmosphere, using
attenuation mean free paths measured directly by the experiment combined
with the very latest data on cross sections, i.e. fragmentation probabili-
ties, not available to previous investigators. New values of 38.5 + 5.2,
32.4 + 8.7, 23.7 + 5.9, and 16.8 + 2.7 g/cm 2 for the attenuation mean free
paths in air for these same charge groups are reported. These data repre-
sent one of the most complete sets of attenuation mean free paths in air
reported to date.
Propagation calculations for 10 Z 28 nuclei indicate that the observed
abundances are consistent with a source composition having Ne/Fe = 1.44 +
0.12, Mg/Fe = 1.68 + 0.08, Si/Fe = 1.38 + 0.05, S/Fe = 0.29 + 0.02, and
Ca/Fe = 0.18 + 0.01, with all other abundances 16 Z 28, which are generally
agreed to be secondary, 0.04. The abundances also have been found to be
consistent with an exponential path length distribution with a mean amount
of matter of 51 01 g/cm2
The source composition is deficient in sulfur and argon relative to the
solar system, pointing to the conclusion that cosmic rays are synthesized
under different conditions than solar system elements. It is unlikely
these abundance differences are the result of propagational effects.
More likely the deficiencies can be explained by differences in the
environmental conditions under which the elements are synthesized. With
most cosmic ray nuclei abundances in the charge range Z = 10-28 known to
an accuracy comparable to solar system abundances, it can be tentatively
concluded that these nuclei originated during the explosive nucleosyn-
thesis stage of highly evolved massive stars, i.e. a supernova origin
for energetic heavy cosmic rays.
Where should the study of cosmic ray physics proceed to from here?
First of all, future work should concentrate somewhat on the less abundant
elements between charges 10 and 28 where more definitive measurements are
still'needed. In particular, the abundances of chlorine, potassium, vana-
dium, manganese, and nickel need to be measured more accurately. Errors
in composition at the top of the atmosphere are the cause of a significant
part of the error in the deduced source composition. Reducing these errors
will help to pin down the type of explosive nucleosynthesis responsible for
the elements in this charge range. This measurement would not require an
instrument any more sophisticated than the one described in this paper,
a multiple scintillator - Cerenkov radiator combination; it requires more
collection time at higher altitudes with improved resolution, possibly
on a satellite. A suggestion for low, medium, and high energy accelerator
experiments is the improved measurement of existing cross sections for
interactions of charges 10 to 28 in hydrogen and air-like materials, and
the filling-in of the gaps in existing cross sections. Argon is a specific
case where there appears to be a discrepancy between its deduced source
132
abundance and the solar system abundance. This discrepancy may be due
to incorrect cross sections for interaction of argon, or incorrect secon-
dary production of argon from other elements.
One of the more promising informational studies includes a measure-
ment of the isotopic composition of cosmic ray nuclei in this same charge
region. The results of a determination of the isotopic composition of iron
bears heavily on the question of how these nuclei were synthesized. For
example, if the Fess isotope dominates over the Fe5 4 isotope in the iron
peak, then these isotopes must have been produced during silicon burning
nucleosynthesis in supernovae as opposed to other types of nucleosynthesis
in which Fes4 would be the dominant isotope. To go one step further: the
relative isotope abundance of Fe56 /Fes8 determines whether partial or com-
plete silicon burning has occurred. This gives some indications as to
conditions of temperature and neutron excess existing during the explosion,
and also indicates whether the explosion was fast on a hydrodynamic time
scale. For if the explosion were quick on a hydrodynamic time scale, then
the material contributing to nucleosynthesis expands and cools faster than
silicon burning can be completed, in which case Fes8 is not built up and
Fe6s dominates the distribution. Isotopic measurements require an experi-
ment that features mass resolution as well as considerably improved charge
resolution. Some such experiments are just now coming into their own
(Webber et al., 1973; Fisher et al., 1973).
An even more sensitive test of path length distribution can be made
by supplementing the meager data that exists on the relative abundances
of VVH and SVH nuclei, Z 30, with more experimental results. Iron nuclei
have an interaction mean free path of about 2.5 g/cm"; lead nuclei (Z=82)
133
have an interaction mean free path of about 1 g/cm2 . Lead nuclei traverse
about 4 or 5 mean free paths in 5 g/cm2 of interstellar material as opposed
to 2 mfp for iron. Mewaldt et al. (1971) have begun a series of measure-
ments of Z 30 nuclei using a multiple ionization counter detector syst'em.
Due to the low fluxes of these elements, their results have not yet provided
a definitive test of the path length distribution but they are consistent
with a leakage length of 5 g/cm2
It is important to point out that differential energy spectra measure-
ments of cosmic rays should be made at many energies, particularly very high
energies of 100 GeV/nuc.or more where recent results (Webber et al., 1973;
Balasubrahmanyan and Ormes, 1973; Smith et al., 1972) indicate the relative abun
dances are not constant with energy, an assumption that has been made by
all cosmic ray physicists in the past for analyzing data. Intercomparison
of low, high, and very high energy results should aid even more in contri-
buting to an understanding of interstellar propagation and delineating
source regions. The change in slope of the spectrum of iron group nuclei
detected by Ormes et al. (1972) can lead to the conclusion of 2 possible
sources of cosmic ray iron nuclei, as pointed out by Ramaty et al. (1973).
Changes in composition with energy detected by several groups mentioned
above, i.e. the decreasing ratio of daughter nuclei to parent nuclei with
increasing energy, can lead to the conclusion that confinement of cosmic
rays in the galaxy is energy dependent. Many experiments can be used to
make these energy spectra measurements: gas Cerenkov counters, supercon-
ducting magnets, ionization spectrometers, most of which are already in use
by the groups mentioned above.
The preceding paragraphs have pointed out some experimental discrep-
134
ancies still existing in the field of cosmic radiation and some experi-
ments which can be performed to resolve these discrepancies and test
the various hypotheses.
It is hopel that in the near future a satellite version of this experi-
ment can be flown so that data collected, away from atmospheric and other
terrestrial effects and with much greater statistics, can be analyzed to
answer these remaining questions, but which, at the same time, will probably
raise many new questions.
APPENDIX A
ELECTRONICS AND THRESHOLD SETTINGS
A.l. Detector Electronics
The electronics system for this experiment can be divided into
four major subsystems. The following paragraphs will describe each
of these subsystems in turn. Block diagrams for the detector electronics
and data handling system are presented in Figures Al and A2.
The coincidence trigger subsystem produces the fast pulse for
triggering the spark chamber and also provides the signal to initiate
data handling. Its associated electronics search for coincidences
between scintillator S1 and scintillator S2. As has been mentioned
previonsly, the plastic scintillators are used to provide a coincidence
event because they produce a fast pulse as opposed to the CsI scintillator
which produces a slow rise-time pulse. A fast pulse is needed to initiate
the spark chamber so that ionization produced by the charged particlh
will not diffuse too far from the particle's path. The gates for pulse
height analysis of the charged particle detectors are also derived from
this subsystem.
Using gates from the coincidence trigger subsystem, the charge
identification electronics subsystem analyzes the pulse height distri-
bution of the incident cosmic ray particles. Pulse height analysis is
performed on all 3 scintillators and the Cerenkov radiator whenever the
S1 - S2 coincidence occurs. Each pulse height analyzer is of the same
design and operated over three ranges of gain. This "3-slope" analyzer
then effectively has a dynamic range of 103 so that it could detect VH
nuclei as well as protons. The basic analyzer is 256 channels and con-
135
r LINEA
PREAMPS A=64
INTILLATOR PULSE STRETCH. 8 BIT 2 GAIN S(O BITS)
ICERENKOV A. S(IO BITS)
OITPN SPARK HIGH VOLTAGE EI
S(2 BITS)
S- UNRM.
CHAMBER PULSER
CsI READOUT TRANSMITTER
DIFFUSION ---- S(IO BITS)
CHAMBER
CINTILLATOR I { H.-- S(IO0 BITS)
THRESHOLDCIRCUITS
SEGMENT IH.A.
SF FLIGHT 3
ELECTRONICS BLOCK DIAGRAMP M.
E ON 7 PAIRS PHA. S(IO BITS)SEGMENTS
S A Electronics block diagramRM.
Fig. Al. Electronics block diagram.
SYNC CODEGENERATOR
STORAGE SAMPLINGREGISTER GATES
23 TYP. CKTS.I I
SPI XMITTERSTORAGE SPLIT
PH DATA REGISTER PHASEENCODER TAPE
& BUFFER CORECORDERHOUSEKEEPINGMULTIPLEXER
RATEMULTIPLEXER
T SPARK TELEMETRY BLOCK12 DATA LINES CHAMBER 12 DIAGRAM
READOUT LINESCONTROL LINES CONTROL
Fig. A2. Data handling and telemetry block diagram°
138
verted pulse analog data to digital data for readout. The threshold
selection ensures that a pulse-height from an event is routed to the
correct range of the analyzer. Each range has an amplifier of gain = 8
over the previous range. Besides the digital data for the actual pulse
height value, a gain bit is also set in each data word to determine in
which range the pulse height event occurred.
The gains of the four scintillators are adjusted in the laboratory
by first locating the Z = 1 peak corresponding to minimum ionizing
muons at sea level. (The gain of the phototubes used should easily
cover the 104 dynamic range of pulse height values needed to record
events for all charges.) The trigger levels are then set at approximate-
ly 1.5 times minimum to decrease not only background but.also inhibit
the large flux of protons known to be present in primary cosmic radia-
tion. This trigger criterion then would accept all nuclei with Z > 2.
The spark chamber subsystem is capable of identifying the tra-
jectory of the incident particles and of distinguishing whether the
event is due to a single particle or multiple particles. The spark
chamber readout time limited the speed of the CIM to 10 events/sec.
The data handling subsystem, or encoder, arranges all informa-
tion of interest during the balloon flight into the proper format
for telemetry and for recording by balloon-borne tape recorders. (Re-
dundancy of data handling was provided in this crucial area for increased
reliability.) The data was handled as a fixed format telemetry frame
consisting of sync pulses, housekeeping data on temperature, external
pressures, etc., and then a series of words filled by the experiment
data. Whenever an event occurs, the experiment data words are filled
by data in a known format. The first word is the time tag to identify
139
an event. The second group of words contains data from the CIM (48
bits). Data from the ionization spectrometer modules then follows
(160 bits). These three fixed-length blocks of words are followed
by a variable number of words of spark chamber data (" 200 bits), and
finally an end-of-event word. This results in 420 bits/event or 4200
bits/sec for events of interest which was transmitted at a 12.0 kbit/sec
rate from balloon to ground via FM/FM telemetry. Twelve hours of
recording time on serial PCM balloon tape recorders was allowed for
this flight.
The PMTs, PHAs and readout logic operate on 45 watts of battery
power. The telemetry and on-board recorder require another 5 watts,
for a total power of 50 watts.
In addition to the features discussed previously, Figures Al
and A2 also emphasize the redundancy which has been built into the experi-
ment to avoid a catastrophic failure. For example, there are two PMTs
looking at each detection element, and there are two complete and inde-
pendent data readout systems.
A. 2. Event Selection: Triggering Modes
The High Energy Cosmic Ray Experiment is designed to look at all
of the various components of the cosmic rays above an energy 109 eV:
the electrons, protons and multiply-chargee nuclei. Because of this
and the large area of the detector, complex triggering requirements have
been set up to select events of interest. Were this not done, the ex-
periment would trigger on the much more plentiful low energy proton
and alpha events. By electronically selecting only those events of
particular interest, the data transmission rate and spark chamber re-
petition rate have been reduced to an acceptable level.
To convert pulseheight values to charge of particles, the one
particle normalization point must be known. The background flux of muons
at sea level provides a convenient means of calibrating the detectors
in units of single relativistic particles, i.e., a minimum ionizing
particle. The peak in the muon distribution gives the most probable
ionization loss. Using this value as the calibration point for the
analog electronics, the channels of the pulse height analyzers were set
such that protons and electrons, both charge 1, were set at 0.3 x
minimum.
There were four modes: electron or e mode, proton or p mode,
nuclei or Z mode, and calibrate or c mode. Only the Z mode is of
interest here so this mode will be described in the following para-
graph.
Whenever the experiment is not in the calibrate mode, it is consi-
dered to be in the experiment mode: any event in the e, p, or Z mode
is classified as experiment mode. However, the experiment mode is
allowed to trigger in the calibrate mode once every 32nd event, i.e.,
140
141
the coincidence requirements for the experiment mode are relaxed and
the first particle which passes through the S1 - S2 scintillator
geometry is recorded by the detector.
The Z mode, divided into a low Z mode and a high Z mode, is de-
signed to be sensitive to any charged nucleus with Z > 2. For the flight
data under examination, the requirements on the scintillators were
simply:
20 x mir > 51 > 7 x minimum
20 x min > S2 > 7 x minimum
C > 6 x minimum
For the low Z mode (Charges 3 and 4 which ar6 not of interest here)
there were no other requirements. For the high Z mode consistency
between the Sl - S2 pulses is required as follows:
Sl or S2 > 20 x minimum
S1 > 15 x minimum
$2 > 15 x minimum
C > 6 x minimum
The requirements for accepting an event and pulsing the spark chamber
in the Z mode are shown in Figure A3.
Z MODE FLIGHT 2 & 3
So>7x --_ ORSI S2>20 x
S S>7x BLOCKLOW Z AND
Cer > 6 x OR Z MODE
S >15x HIGH ZMODE
S2>15x
Fig. A3. Logic diagram showing event acceptance criteria and triggeringrequirements.
APPENDIX B
DEFINITION OF A "GOOD EVENT" IN SPARK CHAMBER
The Master Analysis Tape program reads and unpacks the cosmic
ray data tapes. Included in this data are spark chamber coordinates
describing the incident direction of the charged particles. From this,
an attempt is made, using the criteria specified later in this section,
to determine a trajectory for each event. Determination of a unique
trajectory is impossible for a high percentage of events due to multiple
coordinates in one or more planes or the absence of coordinates in one
or more planes. When a trajectory cannot be determined for an event, that
event is labelled as complex and classified into one of seven different
types. For each of these types more criteria are established and another
attempt is made at determining the path of the cosmic ray particle
through the detector.
Ideally, a particle passing through the spark chamber would cause
a single wire to be set in each plane, thereby resulting in 4 pairs of
(X, Y) coordinates. Unfortunately, in actual operation each spark
chamber plane may have from zero to about seven adjacent or nearly
adjacent wires set by an incident particle. Consequently, the arith-
metic average
nC = ( E Ci)/n (Bl)avg i=l
is used to determine a single coordinate value. Specifically set wires
immediately adjacent, or set wires separated by one or two unset wires
are averaged using this averaging technique. Up to seven set wires are
averaged as long as the two extreme set wires are not separated by more
143
144
than six wires. The following examples in which a + 'indicates a set
wire and an 0 an unset wire would be averaged:
+; ++O+; +,+H ; +OO-f++.
The following examples would not be averaged due to separations of
greater than six wires between the extreme set wires and would be
assigned to one of the classifications of complex events:
++IH+I1+; +00+0+0++.
Even after averaging there are frequently multiple coordinates in
several spark chamber planes. These cases are given critical consider-
ation'in the following paragraphs.
The zero level XY plane of the rectangular coordinate system in
which the trajectory is computed is the Y4 spark chamber plane. The Z
axis is perpendicular to the Y4 plane. The trajectory is computed in
terms of the slopes and intercepts of the projections of the trajectory
onto the XZ and YZ planes.
The projection of the trajectory onto the XZ plane is computed
from the averaged spark chamber coordinates in the X , X2, X3 and X4
spark chamber .planes and the fixed distances between the X planes along
the Z axis. The projection of the trajectory onto'the YZ plane is
similarly computed using the Y spark chamber planes. The following
paragraphs state the methods used to compute the slope and intercept
of each projection for events with various combinations of coordinates.
Case 1. One coordinate per plane is the simplest case. It is
also the ideal event. The slope and intercept are obtained by performing
a straight line fit on the four coordinates. This same method is applied
145
to three coordinates if one of the four planes has no coordinates. The
rbot mean square deviation of the fit-is also calculated. If this value
exceeds an input acceptance criterion, the event is classified as
complex.
Case 2. An event in which more than two planes had no coordinates
would immediately be classified as complex.
Case 3. To analyze an event producing multiple coordinates in
one plane, at least two of the three remaining planes must have only
one coordinate. The other plane could have one or no coordinates. A
trajectory is determined by performing a least squares fit with each
coordinate in the plane with multiple coordinates in combination with
the single coordinates of the other planes. The fit with the smallest
rms is chosen if that rms is less than the acceptance criterion, the
event is classified as complex.
Case 4. When the case of multiple coordinates in more than one
plane occurs, the best fit is calculated using each spark chamber plane,
provided each plane has at least one coordinate. If the rms of the
best fit does not satisfy the acceptance criterion, the event is
classified as complex. If each spark chamber plane does not have at
least one coordinate the event is also classified as complex.
Each event is assigned a simplification level which is a measure
of the degree of difficulty involved in computing a trajectory. There
are 5 simplification levels numbered 0 to 4 with levels 2 to 4 being
sublevels of level 1. Cases 1 to 4 discussed previously are assigned
level 0. Events which are not assigned level 0 but which. satisfy
either of the following criteria are assigned level 1:
146
1. There exists one coordinate in each plane after averaging
and the least squares fit acceptance criterion is satisfied
if one coordinate is ignored.
2. There exist multiple coordinates after averaging in one
plane, and single coordinates in the remaining three planes.
In this case all coordinates in the plane with multiple coor-
dinates are ignored except for that coordinate which results
in the best least squares fit. If this least squares fit
does not satisfy the least squares fit acceptance criterion
but a satisfactory least squares fit is obtained by ignoring
one of the remaining four coordinates, then level 1 is as-
signed.
Level 2 is assigned to an event if a trajectory satisfying the least
squares fit acceptance criterion can be computed subject to the follow-
ing conditions:
1. A coordinate from each of the four planes is used to compute
the trajectory.
2. At least two of the four coordinates used to compute the
trajectory are averaged coordinates.
A least squares fit through every combination of two averaged coordinates
is performed. The remaining two coordinates used in the fit are those
closest to a straight line passing directly through the averaged coor-
dinates. These two may or may not be averaged.
If two fits satisfy the acceptance criterion, their rms deviations
are compared to an internally-defined criterion of 0.05 inches. If
both deviations are less than this criterion then the event is again
classified as complex.
147
If the smallest rms deviation computed as described in the pre-
vious paragraph does not satisfy the least squares fit acceptance
criterion, or if there are not two planes containing averaged coor-
dinates, then level 3 or level 4 is assigned.
A least squares fit through every combination of coordinates not
tried for level 2 is performed. If a satisfactory trajectory. is found
using one averaged coordinate the event-is assigned level 3. If a
satisfactory trajectory is not found using one averaged coordinate
but is found using no averaged coordinates, the event is assigned
level 4.
An example of a well-defined trajectory, in which case the event
is acceptable and is classified as "good," is shown in Figure B1. A
spark chamber track for a carbon nucleus is illustrated in this figure.
The chamber is separated into an (X, Z) view (upper 4 lines) and a
(Y, Z) view. Every 7th line is shown as a dot and each set core is
denoted by a vertical line.
If an acceptable trajectory cannot be found by any of the methods
discussed in previous paragraphs, the event is classified as complex
and must be discarded.
These events fall into one of seven complex event types recog-
nized by the computer algorithm. They are:
1. The particle path does not intersect the coincidence scintil-
lators, Sl-S2.
2. There are no spark chamber coordinates.
3. Three spark chamber planes have no coordinates.
4. The width of a coordinate set requiring averaging is greater
than seven wires.
16 PH VALUES (uncorrected)
336 324 311 74 314 339 324 324 O ) C O , , O16 PH VALUES (corrected)
328 317 310 67 309 332 318 318 O 0 0 . 0 0 e O
EVENT NO. = 0 THETA=2.34989E+01 ALPHA= 1.6534E+02
X- PLANE
* * * * * e. *. * *i * 0 0 * * * * * * 0 * * * * 0 0 * * * * 0 * 0 0 * . . S
00oo
Y- PLANE
ERRX=3.11 53E-32 ERRY=4.34551E-.2OPTIONS:RECALCULATE TRAJECTORY X YSAVE EVENT OLD NEWPROCESS NEXT/EVENTTERMINATE JOB
Fig. Bl. Example of a well defined trajectory through the spark chamber for acarbon nucleus event. Note the satellite sparks near the trajectorywhich are presumably due to knock on electrons. This figure has beencreated from a slide taken of a graphic display unit which can be usedto look at individual events.
149
5. The least squares fit acceptance criterion'is not satisfied.
6. There are multiple coordinates in more than one plane,
and none of the acceptance criteria mentioned previously are
satisfied.
7. There exists more than one trajectory satisfying the least
squares fit acceptance criterion for multiple trajectories.
APPENDIX C
SOLAR MODULATION
In general, the cosmic ray intensity detected near the earth is
depressed below that which would be measured outside the'solar system
in interstellar space. The magnitude of the solar modulation depends
on the level of solar activity; it is probably both rigidity and velocity
dependent, and also reduces the energy of the particles. A completely
adequate theory of solar modulation that will permit the intensities
to be demodulated to obtain the intensities in interstellar space does
not exist. This is due to the considerable amount of uncertainty
that exists regarding the amount and form of the solar modulation even
at times of minimum solar activity where there may be some residual
modulation.
To summarize, two aspects of solar modulation are of importance
in the demodulation of the.intensities measured at Earth to those
existing in interstellar space: the functional form of the modulation,
and the magnitude of the residual modulation existing at solar minimum.
Numerous theories have been put forth in an attempt to explain
solar modulation. Several papers now exist which review and analyze
the models in sufficient detail such that it is not necessary to do so
here. Thus only a general discussion of the problem will be presented
with specific details given only as necessary to the development of
the discussion.
The current state of understanding of these aspects may be re-
viewed in the following papers: (1) Diffusion Convection Theory,
Parker, 1958, 1961, 1963; Dorman, 1960; (2) Adiabatic Deceleration
150
151
Energy Loss Process, Fisk and Axford, 1969; Gleeson and Axford, 1967,
1968 (this model leads to the force field solution at high energies,
E > 1'GeV/nuc.); (3) Statistical Treatments of Magnetic Field Power
Spectrum, Roelof, 1966; Jokipii, 1966. Difficulties with the latter
theory have been pointed out recently by Fisk et al., 1973. The reader
is also referred to several excellent review articles: Quenby, 1967;
Webber, 1967a; Jokipii, 1967; Cleghorn, 1970.
Several important conclusions of the previously mentioned theories
are important to the correction factor calculated in Section III. I.
There are good theoretical reasons,for believing that nuclei having
similar charge-to-mass ratios will be equally affected by the solar
modulation process. When evaluating solar modulation effects, it is
usually considered that all charges with Z > 3 have A/Z = 2; therefore,
changes in the intensities of heavier nuclei brought about by solar
modulation are the same for all such nuclei. More importantly it allows
the results of the more numerous studies of the modulation of helium
nuclei, where also A/Z = 2, to be applied directly to the modulation of
heavy nuclei. (For helium nuclei, A/Z = 1.95, due to a 10% admixture of
He3. For iron nuclei, where A/Z = 2.15, the error introduced in the
correction factor using A/Z = 2.0 is about 4% at the energies under
consideration here. This is well within the error on the estimate of
the amount of energy loss of helium nuclei, with A/Z = 1.95, due to
solar modulation in 1970 which is about 15%.) The only study of the
modulation of VH nuclei substantiates this approximation.
Cleghorn (1970) reviewed the existing theories and concluded that
charge-dependent modulation is not predicted by any of them. He found
the solar modulation of VH nuclei to be identical to that of helium
152
nuclei to within the statistical accuracy of his experiment. In another
study (Garcia - Munoz and Simpson, 1910), IMP-4 data at solar maximum
is compared to OGO-1 data at solar minimum of Comstock (1969). They
find the relative abundances versus energy per nucleon are not dependent
on solar modulation, i.e. all heavy nuclei are modulated the same.
These satellite results are more substantial since they are not subject
to atmospheric problems. An earlier review paper (Freier and Waddington,
1964) suggested the modulation is the same for heavy nuclei as for helium
nuclei, or at least that the process is not strongly charge dependent.
The extent to which particles lose energy as they penetrate
the solar wind on their way to Earth is not accurately known. At
solar minimum the total loss may be 100 MeV/nuc; at solar maximum it
may be several hundred MeV/nucleon (Freier and Waddington, 1965;
Gleeson and Axford, 1968). This ionization energy loss has only a
small effect on the shape of the energy spectrum. Its only effect on
the charge composition would be to shift the energy threshold of the
observed intensities to a higher energy outside the solar cavity.
The most complete theory available for the study of solar
modulation of cosmic rays is the theory which includes diffusion-
convection and adiabatic deceleration energy loss. This problem has
no analytic solution but can be solved by numerical techniques (see
Fisk, 1971; Fisk et al., 1970; Fisk and Axford, 1969). However,
simplifying assumptions result in several analytic solutions: separable
diffusion coefficients of different forms result in analytic solutions
(Urch and Gleeson, 1972; Jokipii, 1971). These authors compared the
results of the numerical solution to the solutions reached from other
theories. The conclude that above about 1 GeV/nuc.the theories produce
153
essentially similar results: Cleghorn (1970) concludes that the diffu-
sion-convection model and force field model solutions are essentially
similar above 1 GeV/nuc., Fisk and Axford (1969), and Gleeson and
Axford (1968) concluded that the diffusion-convection model and adia-
batic deceleration are essentially the same to within + 10%. But more
importantly, Gleeson and Axford (1968), Fisk and Axford (1969), Fisk
et al. (1970), Fisk (1971), Gleeson and Urch (1971), and Urch and
Gleeson (1972), show that above several hundred MeV/nuc the force field
solution and complete numerical solution are very nearly the same.
Since the force field solution is easiest to use, it will be used
by this author to calculate a solar modulation correction factor to
the data presented here.
The force field solution:
where jt(r,E) is the intensity measured at Earth at time t, jo(-,E+@)
is the intensity in interstellar space, E is the total energy of the
particle, Eo is the particle rest energy, and is the mean energy
loss due to adiabatic deceleration, will not be derived here. The
reader is referred to papers where it is derived from Liouville's theorem
(Freier and Waddington, 1965)
D ... o.+.n.. (C2)
or by assuming the cosmic ray streaming is zero (Gleeson and Axford,
1968).
154
S = VU - K -r (c TU) o (C3)
Fisk and Axford (1969) have shown that these two starting points are
mutually consistent by reducing the S E 0 equation to Liouville's
theorem for conservative force fields.
The force field solution directly relates the local intensity to
the unmodulated interstellar intensity. The intensity behaves as
though the modulation were due to a conservative force field that it
dependent on particle energy. Once a value of 1 is determined from
experimental data, the modulation correction factor can be calculated.
An interesting sidelight is to compare-the calculations from
the detailed theory to the old method of using a regression curve.
The regression curve method is detailed in the following paragraph.
A convenient way to represent the variation of the cosmic ray
intensity is to construct a regression curve between the nuclei inten-
sity above some rigidity threshold and the sea level cosmic ray in-
tensity as measured by a particular neutron monitor. On such a regres-
sion plot, the data points should be distributed about a unique curve
within the statistical deviations. The regression curve can then be
used to predict the value of the nuclei intensity at any particular
counting rate of the neutron monitor. Regression curves of the inten-
sities of helium nuclei as a function of modulation as measured by
neutron monitors have been presented by several workers (Freier and
Waddington, 1965; Webber, 1967; Freier and Waddington, 1968; Rygg, 1970).
Figures in these papers show the modulation of the primary intensity as
a function of the Mt. Washington neutron monitor counting rate at various
155
energies, normalized to zero modulation when the counting rate is 2400,
the solar minimum counting rate. The average neutron monitor rate of
2108 for this flight has been found by averaging the neutron monitor
hourly counting rate over the duration of the balloon flight (J.A.
Lockwood, private communication).
Using the results of figures from Webber (1967) and/or Freier
and Waddington (1968) (their results are essentially the same since
the figure of Freier and Waddington is derived from the figure of
Webber), one calculates correction factors of 1.38 for R > 3.25 GV
and 1.17 for R > 4.9 GV.
Since there is little difference between the correction factors
calculated here and those resulting from the regression plot, the author
concludes that no systematic differences should arise in comparing the
present experimental data to previously published data which used the
regression plot method.
One final remark is in order. It will be assumed here that there
is no residual solar modulation at solar minimum, even though the theory
predicts some small amount. It is, therefore, assumed that the values
given in Column 3 of Table 4 are those existing in interstellar space
outside the solar modulation cavity.
Justification for this assumption rests in the fact'that this
part of the theory is yet to be substantiated by experiment. In addi-
tion, interpretation of the data on charge composition depends on the
relative abundances, not on the absolute intensities.
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